Animals' heads (also parts of their backsides, including tails, but most distinctively their heads) can be placed into solid blocks; this is merely a visual glitch. As far as I can tell, this does not cause any suffocation damage. The Player can push them in the walls or they can walk into it themselves. I tested this on Pigs, Cows, and Tamed Wolves (full-size and babies), so I may assume that it happens to every animal. To recreate it all that you have to do is push an animal into a solid block or watch them do it themselves. Please see the pictures.