A while back I was trying to help a stray cat, who turned out not to be a stray at all, but my neighbor's cat. Even though he has a home, darned if he hasn't been trying to wriggle into mine little by little. (I think he's quite neglected - often locked out for days at a time.)
I found myself feeding him, going outside to sit with him on the patio for a nice cuddle (hiding from my neighbor just in case he's the jealous type), and finally letting the cat in as far as my kitchen. Every time, he wheedles to check things out (you know what they say about cats and curiosity), but I don't let him because, 1) I'm afraid he might have fleas, 2) I'm afraid he may pee on things, 3) he's not my cat!
Today, I gave in to the inevitable and let him into my house.
As you can see, he was quite content to visit.
He hung out for an hour or so, slept, ate, then went on his way without so much as a goodbye.