To repro:
Spawn a chicken jockey
Issue the command /kill @e[type=Chicken]
The chicken will die, and the baby zombie will fall into the block that the chicken was standing on, and start to take suffocation damage.
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Duplicate of MC-119

It may not be a duplicate. When these zombies move, they quickly pop out of the block and back on to the surface. I've seen the behavior from MC-119, and the mobs generally stay in the ground. Plus, there's this comment from MC-119.
> Definitely in 14w18a. Had a bunch of baby zombies chasing me inside grass blocks.
If these zombies are not suffocating, then that's another different behavior.

Is this still a concern in the current Minecraft version 14w30c or later? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.

Seems like a duplicate of MC-72868.

Seems fixed in 1.8.1-pre1 (also due to fix for MC-72868).