Or imperforate anus/atresia ani, as is the correct term.
-Here's a scientific illustration.
-Here's a cute video of a cat who received surgery to give him a butthole.

Sometimes animals are born with a malformed or lacking anal opening, which without surgical intervention leads to death within days/after weaning. The one case i've known irl was a puppy born with no tail and no asshole, in a breed that doesn't carry the bobtail gene. This site (contains dead puppy photos) and several others imply there's no imperforate anuses on tailed dogs, but while the two may be linked, i have seen pictures of tailed dogs with the condition still, and the cat video linked above has a normal tail.

All the pictures are pretty gruesome, so google at your own risk.