Let me just say that, having been the victim of stray dog attacks as a child, thank goodness my German Shepard defended me or i would have been seriously injured by 2 dobermans, and the owner of a very strong athetic dog capable of breaking all but chains that each individual link had to be 1/2 inch think and welded shut, that dog attacks are very serious. An improperly feed dog will hunt to fill its belly, and the more it kills and eats its kill the more aggressive it can become. Its like a child learning to walk, the more success it has the more confident it becomes. After a while, larger animals are added to the menu. After that, when a person tries to defend their animal from the dogs attack the dog may be so bold as to fight for what it considers its prey and attack the human. A properly fed dog still prefers the taste of fresh meat over dry dog kibble, they are after all carnivores. And some breeds, like the Siberian Husky, Malamute, and other sled dogs were allowed to hunt their own meals even after domestication. They have a much stronger prey drive, and it is impossible to rehabilitate a Siberian that follows those instincts. I have tried with Sasha, tried desensitizing her to birds, and various other methods that did not evolve hitting her or tieing up a dead body to her collar for 3 days (I believe that it is mean/inhumane with how sensitive their nose is, and I only give 2 fingered corrective smacks, with a verbals command, for things such as "mouthing" hard and leaving marks with their teeth). My concern here is that someday a person will be injured, maimed, or killed because someone "knows" their dogs. I know my dogs and I also know that they could turn on me or my family and treat them with respect. Knowing that some insticts and behaviors cant be stopped i opted for containment, and it has proved to be the right choice. Male dogs will roam looking for females in heat and for food, "bachelor" packs form and become a very dnagerous problem. A female with young will go to extra ordinary lengths to feed her pups. This is why containment is so essential. Do I love my dogs, yes very much, I snugglethem all the time, and many of my past and current dogs were street dogs that I could rehab. My Belgian was a badly abused dog with man agression(now fixed), 1 is a backyard breeder pup that never knew human touch, the feel or grass or what being dry felt like, 1 is a shelter dog who has heartworms and has torn CCL ligament in her right knee, and 1 was a street dog with chicken killing instincts. I have donemy best to give them a good life, despite their bad start. And rehabbing all these dogs has thought me a lot. I am also teaching my children, what I know about dog behavior.
Anyway, if a dog comes killing you livestock, and you make the decision to shoot it, shoot to kill. Do not try to scare it off, or wound it. Put it out of its misery, because most likely it does not get taken care of properly, and it will be back now that your livestock are a food source. I think a clean kill shot to the head is more humane than leaving the poor dog to harass someone else or starve to death. Traps can be used, if your local animal control will come get them. Mine won't, and if we drop off the animal we have to pay a fee.
This is a harsh reality I wish I could change. But I was badly bitten trying to save and rehabilitate a stray dog that was killing livestock. Some just can't be saved, and I blame their "owners".
Sorry for the long post