I have come accross a range of different animals, mobs and villagers that are not moving, BUT an invisible version of the same continues to move, for example I came across a skeleton that wasn't moving then all of a sudden I started taking damage from arrow's coming out of nowhere, because it was, but invisible! I ran away and logged out/in again and I could see the skeleton coming towards me. Same with passive mobs, they just freeze and an invisible version continues to breed for example with hearts coming out of mid air. Logged out or unload and reload the chunks and then they move again.