This could have relevance to dog breeds originally selected for fighting or baiting, then subsequently selected for companionship. Maybe if a fighting or baiting dog is n generations into social breeding it can be considered safe?
So to answer your question in that context: Yes, it would be more than possible to take a population of dangerous fighting dogs and use them as the base stock for a pet breed, provided that the breeding program was well designed. However, the general mutt population will always have fighting dog traits mixed into it so long as there are fighting breeds around.