If you crouch and move to the edge of a block, you won't fall of, but if there is a slab and you move diagonally to the corner of the block next to the slab, and keep moving diagonal, instead of not being able to fall of and going to the slab, you will fall off of the block next to the slab. This is also true if you are on stairs and are moving diagonally from the upper part of the stairs to the lower part.