Igor cannot move over a pit, but he won't fall into a pit either. If you try to move Igor into a pit, he will simply stop. Mummies, vines, and scurries will also be blocked by pits.

Robots will fall into pits. If you move a Helper Robot over a pit, it will fall into the pit. The Robot will still be active, bumping away at the bottom of the pit.

Carts can be pushed into pits.

Cheese and monster parts can be moved over pits, they are too large to fall into a pit.