greybeard
Herd Master
Things are a little different here.If a neighbor's dog got in and killed or injured livestock, I would catch the dog, return it to the owner and demand payment for the loss.
My neighbors and I are all in 100% agreement. Any of our dogs chase, harass or kill any of each other's livestock, they're toast. Any deviation from that would be an unexpected courtesy and the only favor I and my neighbors have asked is to let each other know so we can come pick up & dispose of the body same as would be done if it died of natural causes on our own property.
That may seem cruel, but the fact is, if a (my) dog will cause harm to someone else's stock, they will also do it to that of the dog's owner if he (I) isn't around to prevent it.
Having said that, most dogs can be trained not to run livestock, but they all still have the ancient instinct to do so. So far, I haven't lost a dog due to livestock harassment, they pretty much stay home.