My little sister has gone through a problem years ago. Not with a yorkie but a puppy. My crazy neighbors across the street have gone through so many dogs over the years you never really see the same dog two years in a row. They just let roam the streets and they disappear. About six years ago my sister and I noticed a little white and black puppy roaming around my yard. Poor thing wasn't acting like a puppy should so before my sister left for the night she took the puppy with her. I got a call a few hours later that she had had to rush the puppy to the emergency vet. The puppy had so much worms in her she needed a blood transfusion. If she hadn't taken the puppy that day the puppy would have been dead the next morning. A few days later she came back and went and asked the neighbors if the puppy was theirs. It was and they wanted her back til my sister told them all what was wrong with the puppy. They told her to keep the dog. Now Lucy is one of the best dogs I have ever known.
My opinion is it is better to ask forgiveness than permission.
It drives me up the wall people just let their dogs roam free. I would lure those poor babies off and say I found some strays put flyers up and see if those people respond.