Many, if not all, the Junkyard Dogs were once house dogs.
Think about it. Most of them have easily recognizable breeds (sheepdog, Afghan hound), when was the last time you saw dogs like those on the street? It is more likely they were abandoned by their owners (street dogs being usually of no breed). Buster was once a house pet
It is a secret of him, but he was abandoned on the street by his family (following the example above, when was the last time you saw a Doberman/Rottweiler mix on the street and what are the odds?) when he was younger and met Tramp, who helped him survive (Mooch does say Tramp taught Buster all he knows). This is also one of the reasons why he shows such a reaction when recalling that Tramp now has a family and "free room and board". It isn't just that he feels abandoned by his mentor and friend, he also resents that Tramp has the nice life he lost. Buster does have an owner
But he was bought to be a guard dog for the junkyard. He is resentful because despite having an owner, he doesn't have the love that other dogs with people get since his human sees him only as a tool to protect the junkyard.