Please don't feel bad. MY cats roam, and they DO NOT wear collars. This is because the 2 new young ones are ferals, that have never worn and will not wear LOL collars. Goose simply gets his off in minutes of being outside. Can't tell you how many dollars i've wasted. Ditto Laphrogie. My other cats that disappeared were the same. One did wear, and I after 9 collars were lost, stopped trying to impose.
After losing the 2 cats, I decided that the next cats would be chipped.
maybe even an ear tatoo too... that way people know they are owned and cared for, even if no collar on. Goose simply won't wear one. Frogie, will, but then takes it off too. My oldster Diablo has the same collar he's worn since 1999!! Amazing. He has NEVER not worn a collar. Shebs used to wear, but no longer goes out and shows no interest, so no collar.
My advice - if you see a nice kitty coming round to eat - let it eat, but if it looks groomed and fed, and wants outside its probably someones cat.
Some cats are "visiting" cats they are social and like to visit other people's homes. (Diablo would do that when young...) If in doubt, take to vet and have scanned for a chip...
I never took in and kept inside a cat that strayed to me - I always gave them the option to roam, in case they belonged elsewhere. To my knowledge, I never "stole" or "took in" a cat that was owned elsewhere.
That said, don't feel bad at all. You were helping that cat, and he liked
to visit with you!
And sometimes cats just leave their owners to findnew ones, because of dogs, new pets, new babies etc....