In the twin paradox does the returning twin also come back permanently length contracted flatter than the twin on Earth? This video from Brian Greene suggests this is so:
https://www.youtube.com/watch?v=2sZUNud6rRw&list=PLj6DWzIvBi4PFDXCCV1bNhVUgDLTwVbFc&index=60
It shows if you stop a pole in the barn (ignoring all the obvious engineering challenges of doing so) it will end up permanently length contracted just like the returning twin will end up permanently younger than her earth bound twin in the twin paradox. Ignoring the practical problems with infinite deceleration, she stops when she turns around and that causes her permanent age difference but does she also end up permanently flatter? Again just consider the relativistic math and not all the physical impossibilities this example entails.
Relativity allows a frame jump without deceleration, it's called a clock handoff in the twin paradox. Since a clock is used to measure length for length contraction, a clock handoff could also keep a record of both permanent age difference and permanent length contraction when the twin hands off her clock readings to a ship passing her to return to earth. There's no physical crunching of the pole in a clock handoff.
So does relativity sanction permanent length contraction along with permanent age difference in the clock handoff twin paradox?
 A: No, length contraction occurs only while there is relative motion, so assuming the travelling twin comes to rest in the frame of the stationary twin, they will once again agree that they are the same length. 
The age difference is not a permanent time dilation- the clocks of the twins will run at the same speed once they are back in the same frame.
You should also remember that the effects are entirely symmetric, so that the stationary twin appears shorter to the travelling twin. Ironically that means that even if the length contraction were permanent (which it isn't) there would be no way to tell, as each twin would believe the other was permanently shortened by the same amount.
The scenario Brian Greene is asking you to imagine is one in which the people in the barn apply forces to the pole to bring it to a halt. They think they are bringing all parts of the pole to a halt simultaneously, so that the front of the pole is halted at exactly the same time as the rear.  They believe that because they are applying the forces all along the length of the pole at the same instant they are not changing the length of the pole but are simply capturing it as is. 
However, from the perspective of the pole the forces are being applied out of phase, so when the first grab is applied at the front, there is no restraining grab on the rest of the pole so it continues forward ploughing into the front and thus compressing itself. His example would have been clearer had there been just two people grabbing in the barn, one at the front and one at the rear.
Either way, the shortening of the pole has been made permanent by compressive forces being applied by the people in the barn. If the grabbing had not occurred the pole would not have been physically shortened in its own frame of reference.
A: 
Does relativity sanction permanent length contraction along with permanent age difference in the twin paradox?

No, it does not. However, given the many analogies between time and space this may seem disturbing. What makes time different from space in this context?
The issue is that a clock does something different than a ruler does: it maintains a record. A ruler merely measures the distance between its endpoints, and as a moving ruler is brought (gently) to rest that measurement agrees with a permanently resting ruler. 
The device that most closely resembles a ruler for time is not a clock but rather a metronome. There is no permanent time dilation for a metronome, and as a moving metronome is brought (gently) to rest that measurement agrees with a permanently resting metronome. In this way it is symmetric with the impermanence of length contraction. 
If you want a device that resembles a clock for distance that would not be a ruler, but rather an odometer. An odometer maintains a record and will register permanent length contraction in the same manner as a clock. 
In this way the symmetry between time and space is recognized again. The difference was not due to differences in the physics of time and space, but rather differences in the measuring devices. We were comparing a memory-less device for space to a device with memory for time. With a proper comparison of similar devices the issue is resolved.  
A: No, length contraction is not permanent. The travelling twin ends up permanently younger, and the spatial analogue is that she has permanently travelled a longer distance than her twin. The temporal analogue of being permanently length contracted would be permanently aging more slowly, but neither of these things happen.
Also, the pole in the barn doesn't end up permanently length contracted either. The true answer to the pole in barn paradox is that when you try to bring the pole to a halt inside the barn, it will collide violently with the barn, causing one or both of them to break. The pole is only permanently length contracted in the sense of "shattered into multiple pieces". (According to special relativity, infinitely strong materials are not only practically impossible, but theoretically impossible.)
A: First:  Despite appearances, this question has absolutely nothing to do with relativity, because it asks about the length of a traveler at various stages in the journey with all measurements made in a single frame (namely the earthbound frame).  So the entire question comes down to:  Does decelerating change your length?
The answer entirely depends on how the traveler twin decelerates.  Suppose he's heading toward earth head-first, and he abruptly stops moving.  If (in the earth-frame) his head stops before his feet do,  he's going to contract.  If his head and feet stop at the same moment, he's going to remain the same length he  was while traveling.  If his feet stops before his head does, he's going to stretch out.  
Of course all the same things are true in the traveling frame.  It's perfectly possible, for example, that his head and feet stop simultaneously in the earth frame but non-simultaneously in the traveling frame, so his length stays fixed in the earth frame and not in the traveling frame.  Or vice versa.  That's where relativity comes in, but it has nothing to  do with the question that was asked.
A: Ok, someone has explained this to me on another forum. When a frame jump occurs, time and space effects are no longer reciprocal. Only one participant ages less but the space imbalance is in the distance travelled, not in a permanent flattening of the returning ship. Hence if a non-time based odometer could be made, it would record the ship has travelled a contracted distance but you could not expect the return of a flattened ship because that would make the space effect reciprocal which it no longer is due to the frame jump.
A: I slept on it and came up with a partial answer. As I said I spoke with Don Lincoln years ago on a forum and he impressed into my brain that space and time are two sides of the same coin; whatever problem you can solve using the time phenomena of relativity you can also solve using its symmetrical counterpart space. So I decided Greene's example was the space equivalent of the muon example. 
A spacetime path must begin and end with the participants co-located. The muon's path does not begin co-located with earth, so the clocks are not sync'd, and there is no frame jump (only constant velocity) in that path. Hence, even though the muon ends up co-located with earth, there is no permanent twin paradox age difference. In fact any clocks that co-locate must have the same clock reading unless a frame jump has occurred. 
So in the classic twin paradox example of Alice going and returning at .6c 3 ly out, Bob on earth will age 10 yrs and Alice only 8 when they re-unite. That age difference will be seen in a spacetime diagram. In the muon example, since the clocks did not start co-located and no frame jump occurred, the two clocks will not indicate that the muon aged less a la twin paradox but that its time dilated from an unknown start time. The spacetime diagram should have no difference between the clocks at co-location. Please don't confuse permanent age difference of 1 participant resulting from a frame jump with the reciprocal time dilation of both participants due to constant relative velocity. 
Greene's example is very similar to the muon. The pole starts out unsync'd to the barn clocks so there can be no discernible permanent length difference when it's stopped in the barn. Just like the muon, there is a crash at the end but that doesn't constitute a frame jump when the clocks are co-located. A frame jump has to occur at an appreciable distance for there to be permanent effects on either the moving frame's time or space relative to the stationary frame which is chosen to be the barn in this case.
Greene's analysis may be wrong but what if he had properly done it for a true twin paradox example with a valid spacetime path. He'd have to start the pole and barn together, the pole then goes out and returns to the barn for a valid spacetime path. The pole would have to be permanently length contracted at the turn around point, not at the barn. One thing he did get right was the length contraction is not caused by a physical crushing of the pole but by the incremental relative simultaneity of the clocks as the pole is being stopped by subsequent hands.
Like I said, the clock handoff scenario of the twin paradox involves no crushing of the pole only the effects of relative simultaneity on measuring the pole's length. In the clock handoff, Alice going out meets Charlie returning the pole's measurements (not a physical pole) for her. Neither Alice or Charlie are affected by a frame jump but the data passing between them is. 
Charlie coming in from deep space towards earth has no sync'd clock to earth's clock. He is the muon example incarnate. He sync's his clock to earth's when he gets Alice's clock data. Since neither Alice nor Charlie experience a frame jump, they do not experience a permanent age difference to earth, they just experience reciprocal time dilation relative to earth's clock. What does experience the frame jump is the data. So the data doesn't really represent that either Charlie or Alice have aged less during their journeys. All Charlie has really done is drag a distant time reading into the co-located present with earth when he reaches it. He has aged normally and earth can't really tell he has aged slower, only that his inherited clock data from Alice has aged slower.
So the question is has time and space itself been warped to cause the clock to take real measurements of time and length or has the info of time and space been warped by the delay of distance and the effect velocity has on rate of returning information. For example if a clock face were receding from you, the info from the clock face would have a rate of delay which you could easily misinterpret as time itself being slowed. If only the info is getting distorted, is there any real permanent age difference and permanent length contraction that comes out of a frame jump? Those who answer only permanent age difference is real are forgetting that there's a symmetry between time and space and their position breaks that symmetry. Relativistic effects can only be calculated for either space or time. The muon doesn't cross the atmosphere length contracted AND in a dilated time, it's one or the other. So if permanent age difference does exist according to the twin paradox, then the twin can't also return concurrently flatter as well, it's one or the other. That's my answer interpreting relativity but I'm now personally leaning to the belief that neither occur just as neither really occurs in the clock handoff example. 
PS. No I'm wrong in my last paragraph. The muon example proves that it's not just the information of its clock that velocity affects, it's time itself that the muon's clock measures. Otherwise the muon would not be able to really make it to earth.
A: To my understanding, it does neither.  Special relativity says that if two entities are traveling at a high relative speed to one another, each will observe the other as changed in time, length, mass.  This precludes the goofy idea that one of them will be younger than the other when the velocities reverse and then stop (become non-moving relative to each other.  
Furthermore, if I leave earth and return, I am not at a constant relative velocity, so does special relativity even apply?  So, who’s wrong, me, or dozens of sci-fi writers?
A: No, because the length difference is essentially an optical illusion. It happens because of red/blue shift as an object moves toward or away from your perspective. It is only dependent on the direction of travel relative to you, and only happens in that dimension. An object moving toward you appears thinner, it does not also appear taller or wider. That's why you only get frequency (red/blue) shift and not amplitude shift.
The key is that time, the 4th dimension, changes on us constantly. It's always getting larger (more nanoseconds since the big bang, never the same amount, never less). We progress along the timeline. A clock measures the velocity of this progression (in my timeline, I read my clock as progressing at 1 second per second; if I watch my twin's timeline, I read their clock as progressing at 1.2 of their seconds per 1 of my seconds). Thus, the clocks are a record that they once traveled at different rates. 
E.G., two cars pop into existence with 0 miles on the odometer, going 30mph. One accelerates to 100mph, then they both drive around for 10 minutes, then they both stop at the same spot. They are now both going 0mph. But one car has more miles on its odometer, proving that car traveled faster than the other one at some point in the past.
The fist 3 dimensions of X,Y,Z (length, width, height) are static. The X axis does not continually grow or shrink on us. We do not progress along a size-line. Thus, there can be no record that the twins progressed on that line at different rates in the past.
If we did progress on a size-line, then yes, it would be obvious that they had moved at relativistic speeds in the past. One would be much longer, or wider, or taller, or just overall bigger (larger in all 3 axes) than the other. Their rulers would be different sizes.
