I have my base underground, (Y:35) and I tried to take a few animals like a wolf and cow underground for breeding.

When from Y:40 and below they do this weird falling glitch. They appear to fall and all I see is their head poking out of the floor.

The only time I've had it occur is when they get below the 40 mark. It happens more with Cows and Wolves but it still happens with all animals.
After some time underground they do correct themselves.
Also mobs don't seem to have this problem.