Do non-account NPCs count toward puppy slots?

What about an exception for puppy deaths the day of birth? Say, a litter of four but two are born dead? That wouldn't mess with the numbers too badly.

I dislike exceptions, full stop. But I feel like a puppy that dies the day it's born could count as a stillbirth (even if that's not technically [or politically] correct) and those wouldn't count, in my opinion.