The bug

Mobs can intersect with blocks, which are right next to the mobs, when the chunk they are in was previously saved and is now loaded. This can cause the mobs to suffocate and die or to escape enclosed areas.

Reasons

This is a list of all (possibly) reasons which can cause this bug. These reasons do not exclude each other.

Bounding box precision loss

Caused by floating point inaccuracies, first described in this comment.

Explanation of bug and fix (Worth reading!)

Mobs moving in unloaded chunks

See Markku's comment but might not happen, see this comment.

Baby mobs growing up