If you quit the game while standing precariously over a ledge, when you reload, you'll fall off the ledge immediately. I expected to reload exactly where I left off.

This occurs in creative and survival single player, I have not tested multiplayer. It happens with or without using sneak, but sneaking is a good way to walk right to the extreme edge of a ledge. The ledge doesn't need to be any more than 1 block high (but with more height it's easier to see the bug). I'm not quite sure how close to the ledge edge you need to be or if this works the same in all (N/S/E/W) directions.

My device is a Samsung Galaxy S4 Android 5.0.1 running MCPE 0.12.1.