Could an asteroid land slowly on Earth's surface? The concept in my mind is that an asteroid is on a vector similar to Earth's, but slightly slower (e.g., 50kmh slower). As Earth passes it, it enters the atmosphere at a sharp angle, and since Earth was passing it, it just barely touches down due to Earth's gravity and atmospheric drag.
Given a large asteroid (e.g., 500 meters wide), is there any reason something like this couldn't happen? And, is there any evidence that it has happened? 
 A: Well, technically, the answer is no as the other answers and comments also say.
The approach speed can not be less than escape velocity.
But in order for such a thing to happen, nature has to be really creative and totally in our favor. For example, the asteroid can have a very very lucky combination of these:


*

*The asteroid has right kind and amount of fluid in it that starts jetting out steam at just the right times and right angles.

*The asteroid is parachute shaped with appropriate strength and falls at an appropriate angle.
Again, it would be a miracle, so, please do not hit me. 
As we may be lucky due to a three body interaction with moon, this is taking the luck to kind of extreme. 
A: If the asteroid is in parallel to the orbit of the earth and at rest it will feel the gravitational attraction and will fall with velocity growing as $g\cdot t^2.$ This force will be there whatever the angle and velocity of the asteroid, centrifugal forces may make it miss the earth in a parabolic orbit, or be caught in an elliptical as the path of the satellites. To avoid falling on the earth with great velocity it would need not only to have a small velocity relative to earth but also an acceleration equal or larger and opposite to the acceleration of gravity.
A: The answer is yes.  All it takes is for the asteroid to come at a tangential velocity equal to the "orbital" velocity of an object "flying" at a height equal to (radius of the earth + radius of asteroid). Of course, there are other effects that are being ignored to simplify the answer. 
