I think this could happen if the force exerted by the toupee on the person's head was less than the force exerted by the elevator on the person. The force exerted on the person is due to the rapid change in direction of the acceleration of the elevator (it is accelerating upward, and then rapidly changes the direction of the acceleration to downward).

I guess if the toupee weren't properly attached, and if the elevator stopped quickly the toupee may lift off the man's head. Since the elevator is in a state of freefall for a moment the toupee would lift off the man's head for a moment before the elevator stopped. Since objects can appear weightless when an elevator is in free fall, Walt Disney World requires passengers of the "Tower of Terror" to secure belongs, and put a bar over their laps before the free fall in the elevator.

Yes I would say it could. The mass of the person is greater then the mass of the toupee. Therefore it would require a greater amount of force to move the person in the elevator the the toupee. So the force of the eleveaor rapidly stopping could cause just enough force to life the toupee but not the person.

I think this could happen without the man being tied to the floor. If the toupee was loose enough on the man's head, being a lighter object, it would travel up longer before coming back down, whereas the man would come back down quicker because of his heavier mass.

I don't think many elevators can go that fast. I've been on some pretty fast elevators and my toupee is still right where I put it every morning. Theoretically it can happen. This is because of the law of inertia. A body in motion will remain in motion and a body at rest will remain at rest unless acted upon by an outside force. The toupee is in motion when the entire elevator is in motion. If the elevator comes to an abrupt stop, the tendency of the body as well as the toupee is to remain in motion. If the body is tied down, an outside force is halting it's upward motion. To avoid embarassment, a loop of rope should be run over the subjects head, thus providing the outside force necessary to counteract the inertia of the toupee. It should also be noted that for the body or the toupee to go airborne, the acceleration upward must be greater than the downward acceleration of gravity.