I have a neutered male black mouth cur and live in the sticks with one neighbor. My dog does not go off my property even when her dogs are out. His name is MF Jones and he excels at keeping things that don't belong off of our property. She (neighbor) had to put in an under ground fence to keep her dogs on her property because they would come over and one, a male coon hound, would end up fighting with my dog. Nothing serious ever happened as they are all fairly large dogs, 80+ pounds. My dog was the better fighter and never got injured but I didn't want any of them to get injured. Once her fence was up things were good again.
That said, I have had to pay two different vet bills for two small dogs that were injured by my dog. One on my property and one at a park where both dogs were off leash. In both cases the two smaller dogs started the trouble and my dog finished it. I felt it was my obligation, especially the one at the park, to pay for the vet bills which cost me nearly $1000.
Incidentally, both the smaller dogs were Jack Russel terriers and both male. I don't get what makes them think that they are a match for another dog that is six times their size? They should be called Kamikazee terriers.