This kitty chose you. That's that as far as the kitty is concerned. I have dealt with it both ways. Long ago we had a big beautiful, longhaired kitty named "Clarence" (what was I thinking). Back then I hadn't gained the mature sense that you kept your cats INSIDE. Well, even though he was spoiled, had access into the house all the time, and was greatly loved, he found an elderly lady down the street that he fell in love with. We tried bringing him home several times, but he wanted to be with her, so we let him go.
Then more recently we had a neighbors elderly cat move in with us. She was very old and they didn't provid a warm place for her. We were honest with them about it of course, there were children too, they agreed to let her stay.
It just goes both ways and the welfare and happiness of the cat is the most important.
Good luck! Darrolanne from CA