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We have dogs that are accidentally free-roam. I put up a fence. They jumped it. I raised the fence. They knocked it down. I reinforced it, and they broke the gate instead.
My dogs aren't dangerous. They listen and mind, except when being yelled at to leave the fence alone. They're gentle enough to trust with an infant, and animal-safe enough that not only are our cats safe, but they don't even try to hurt the field mice they play with. They just like to roam.

If a neighbor shot them, then that neighbor better hope his dogs never got out. I've had one that tried coming onto our property to challenge/attack us and our dogs, but I just ran him off. That dog's never been back. Other dogs have come by, but they get run off too. The neighbors do the same for us and our dogs.

Legally, if someone shot our dogs for coming onto their property, there's nothing we could do. Likewise, if I shot their dogs on our land, they're without legal recourse. But this isn't a good way to win friendly neighbors.

For what it's worth, the only dog to challenge/attack on our own property (and the street, etc), is a big Golden Retriever from up the road a bit. The pit mixes, shepherds, rottweilers, etc., have just wanted to play, but that retriever was the only one I'd classify as "dangerous." So much for dangerous/safe breeds.