What happens if a parachute does not open while skydiving?
The majority of the heat developed during reentry of a space-vehicle comes from air compression not friction. Remember, to go into space, you don't have to go very high, but to orbit you will have to go very very fast, and it's not the fall that produces the heat, it's the slowing down part.

If you had a human fall without a chute, the terminal velocity (where air resistance cancels gravity and you continue downward at a constant speed) would be around 100-200 mph, not nearly enough to cause any kind of heat (or cars would burn up by going normal cruising speeds). To get higher terminal velocities, you'd have to go a lot higher, where the air is a lot less dense, higher than any skydiver have, and as far as I can tell Felix Baumgartner did not experience any incineration during his jump.

The unfortunate skydiver will almost certainly die, but there'd definitely be a body, and it'll probably be in one piece.