Three of the cats I had while living with my folks were originally strays.
Two were tamed, moved in fairly quickly, and lived long and full lives, though one preferred to stay a stray and disappeared within a year or two.
A dog that my folks got while I was in college was from the pound, but had a lot of anxiety around people and may have been difficult for someone else to adopt. She was always anxious, especially with car rides, but otherwise had a long and normal life.