If that situation were to happen, it would likely mean that my dog wasn't all that bonded to me. I can't imagine it happening but if for some reason it did, I'd have to seriously consider if it would be a better home.
One of my previous adopters obtained one of her dogs this way. Her Ex lived with his Mom and they had a Shepherd. He passed away and after that the dog kept escaping and showing up at the adopters house until one day his Mom asked her is she wanted the dog because the dog clearly wanted to be there.