I have no experience with car elevators. But pedestrian elevators (in my experience) use either limit switches or a vector drive to determine when to stop raising/lowering. For an elevator that only has 2 "levels," I would assume a limit switch is used.

A limit switch (in this case) would be a normally closed switch that lets electrical current pass through. It would be installed on the vertical legs on the outside. When the floor of the elevator raises or lowers, it rides along the tracks on these legs. Eventually the floor scrapes over the limit switch and pushes it to the open position (no current can pass through). This interrupts the circuit and stops the motor from raising/lowering the floor any further.

Considering how cheap limit switches are, I would hope they put 2 of them on these installations for a little redundancy.