I punched a bully in the stomach at school (after many months of the school doing nothing to address it), and after that he completely left me alone. It was a small school, so I'm fairly sure he didn't move on to anyone else either. A few years later, we even became friends, our younger siblings (5 years younger in each case) become friends (without knowing about the incident in question), and since starting his own company has done paid work for our family (which we wouldn't have allowed had there still be any animosity).

I've no doubt violence begets violence in most cases, but it can also improve the situation for both sides in others.