We had a cat, 30 years ago, that just showed up at the door one day, out of nowhere, walked in like she owned the place, and decided to stay. She lived there for the next five or six years and died. Would bring up snakes and birds and stuff and put them on the front door steps at night.........
I know two cases where a cat showed up and just decided to stay - and in both cases, eventually brought another cat-friend to stay as well. The family I knew that this happened to ended up finding a home for the second cat. But the widow I know this happened to kept both cats (and she had a dog) and then the alpha-cat broght a 3rd cat-friend to stay. I think she found another home for that one.