Is it possible to create a parachute large enough to stop all velocity? This idea came to me while playing Kerbal Space Program. I noticed that the larger my parachute was, the slower my rocket would fall back down to Kerbin. I would like to know if it is possible to create a parachute so large in the real world that it might stop all velocity, essentially making whatever is attached to it float in mid-air. Common sense is telling me "no," but I could always be wrong, and I would love some explanation behind whether or not it is possible. 
 A: It could be possible if the parachute was very large, rigid, shaped like a floating object, and you started descending from the vacuum of space. In this case the parachute would float on top of the atmosphere. It's easier to visualize if you imagine the parachute being a boat and you fell into some water; the boat would float on top of the water and reduce your velocity to zero.
A: No. All parachutes, whether they are drag-only (round) or airfoil (rectangular) will sink. Some airflow is needed to stay inflated, and that airflow comes from the steady descent.
Whether your net descent rate is positive or negative is a different question. It is quite easy to be under a parachute and end up rising (I have done it myself), you just need an updraft in excess of your descent rate. Never lasts though, as a permanently floating parachute would violate a couple of laws of nature.
A: The closest you are going to get is a parachute large enough to slow your descent to the point where you can find lift in rising air and climb away.
They exist and are called paragliders! Strictly speaking they are still falling at 1 to 2 metres per second but rely on rising air ( thermals, ridge etc ) to 'fall' slower than a parcel of surrounding air.
Some large cumulonimbus clouds are big enough to even 'suck' up a normal parachute and I have flown under big storms that appear to be sucking so hard that a bag of cement would stay airborne!
But in still air you are stuck with air flow causing drag so movement of some sort is required.
A: Without the ability to change the shape of the parachute, no.  With the ability, yes - briefly.
A modern square parachute acts as a wing, producing enough lift to slow the descent of the vehicle, but it relies on forward momentum to do so and to remain inflated.  If the trailing edge of the parachute is pulled down quickly, the air moving under the wing will be deflected down, generating a lot of lift for a brief moment.  This is called "flaring".  With the right training, under the right conditions, a parachutist can stop themselves dead in the air relative the ground.  Doing this right before you hit the ground is the trick to landing on your feet.
A: I will answer "yes" if you think out of the box for a parachute, which is a way for a person ejected from a plane to fall on the earth safely.
Theoretically, one might design a parachute with a layer  of helium so as to match the parachute and person downward gravitational force at a certain height, possibly 4 km above ground so as to avoid mountains, with an upward buoyant one. The helium could be compressed and released in the parachute when pulling a cord while ejected or falling.
Of course it would be of no use as a parachute , unless one slowly emptied the helium controlling the rate of fall.  (It should  also have the parachute usual shape and strength as a backup in case the system did not work for some defect).
Helium is very expensive. One could ignore the explosive danger and use hydrogen , after all it could be compressed in a strong enough module not to present problems during normal flights. Such a parachute will ensure a safe landing as the person could choose the spot to land by slowly deflating the parachute/balloon and drifting to better spots.
A: It would be possible in theory, but only in a very side-thinking way: if you make a parachute so large it encapsulates the whole Earth, it will in effect act as a balloon and not fall down, due to the internal pressure of the atmosphere.
This wouldn't work in practice for obvious reasons, but maybe in Kerbal you might be able to do something like it..
A: A parachute is a device specifically designed to create viscous friction.
Viscous friction generates a force that:


*

*is oriented opposite to the velocity;

*is proportional to (a certain power of [*]) the velocity.


So the falling velocity will increase until the drag force (pointing upwards) becomes equal to the weight of the falling object (pointing downwards). This equilibrium velocity can be reduced increasing the drag, but cannot be killed completely (unless you have infinite drag) because this would kill the drag force.
If you want to stop the motion you need another force, this can be the buoyant force (but then you have an aerostat). Another possibility is to have an upward air flow, then you will be falling with respect to air being steady with respect to ground.
[*] Typically $F\propto v$ for small Reynolds number and $F \propto v^2$ for big Reynolds number
A: Yes it is possible. The trick is to have a parachute which is large enough that it's Schwarzschild radius extends down to the object it is lifting.
Under such a circumstance, the parachute would stop ALL motion of the object it is lifting.
PS I just watched Interstellar :D
