I do know of a puppy that had a prolapsed anus, Smiley, but I'm not sure if that pup was hunching and squatting. The surgery was done and I know it was successful, but I'll see if I can find out about behavior before the surgery was done and get back to you.
"We are--each of us--dying; it's how we live in the meantime that makes the difference."
"It's not what you gather, but what you scatter that tells what kind of life you have lived!"
"Be kinder than necessary, for everyone you meet is fighting some kind of battle."