This guy appears to have broken off a rope . I prefer not to call animal control and could please use some advice

I gave him some food and water . I really don’t want to call animal control because around hear they will put him down if not claimed . He is certainly well groomed and very friendly. Even my dog that absolutely despises other dogs was cool with him . I live in a rural area and don’t know any of my neighbors.Any suggestions on what to do is appreciated and can anyone tell me what kind of dog he might be ? Thank you