After you complete this (quite hard) puzzle, you are supposed to drop down onto it and continue forwards.
However, in some games it may instakill you as soon as you touch the broken elevator.
There's no consistent solution to this problem. Things I've tried that have worked:
- Climb the box on the right (which you used to remove the first gear), then leap down and just barely clear the broken elevator and land on the lower platform.
- Jump down from the third floor and land against the wall closest to the starting area, then walk normally across the platform.