Here's what'll happen.
1. The elevator wouldn't continue accelerating forever. It'll have some terminal velocity that I'd estimate to be approximately 150 km/h downwards (think, the elevator isn't exactly the most aerodynamic thing in the world, and a skydiver has a tv of about 200-250 km/h IIRC)
2. You would definitely be on the floor of the elevator and have some weight by the end of the trip. It wouldn't be a true free fall because the elevator has reached it's drag-induced terminal velocity while you haven't (because there wouldn't be any air rushing by YOU, you wouldn't feel a drag force that would keep you at the same tv as the elevator). At the beginning of the fall, when the drag on the elevator is negligible, the motion would approximate a free fall, but once the elevator picked up some speed, you'd regain partial weight and drop to the floor.
3. If there was some kind of glass floor, and you had impeccable timing, you could jump just before you hit the bottom of the shaft and you would definitely make the landing easier on yourself. Heck, if you had strong legs, timed it perfectly, and the elevator wasn't going extremely fast, it'd feel as though you just dropped into a crouching position from waist height.