Where we live, people shoot dogs that go after poultry or livestock. No questions asked. It's understood that you are responsible for training/controlling your dogs.
Where are you at?
Here - the ACOs are stretched to the limit at times and at others, just don't seem to want to do the job (not sure how they got hired). We've had packs of DOMESTIC, "pet" dogs, in our county, take down not only small animals, but horses, cattle, goats, mini horses and couple of years ago - turn on children/families in our county. Wasn't until turned on the children/families - that something was done. Separate packs - one had 20 dogs in it ranging from toy size to larger than our shetland ponies. THe pack that turned on the family had only 5 medium & large dogs in it... Several animals were wearing rabies tags AND had been microchipped. Several owners were found in different states than here, while others were local.
I am previous military, from a military family w/ others currently in the military. I grew up traveling from base to base before we settled in CO for the late teen years before becoming an adult. Rules/laws were so DIFFERENT then than they seem to be now. They also appear to be different in each county in each state as to how these situations are handled...
These days, A lot of pets are just "left" when military picks up and goes - when there is a reduction of forces, or right around Christmas, when there are lots of PCSing going on - pets are abandoned left & right here. See huge increases in animals in the rescues/sanctuaries/"pounds" at those times - the ones that get turned in. Others - you see coursing about - often starving and in bad shape - both dogs and cats. Our new "farmette" is further out in the country w/ fewer people around (larger tracts of farm land than where we were previously) but I'm seeing more stray/feral cats and dogs out here than I did when I was closer to "town" or other communities. Think it's because of being able to "hide" and also to hunt to feed themselves on the other wild life (or our chickens!!).
My chickens get less free ranging on our 21 acres here than they did on the 8 acres we had previously - simply because of the loose "pet" animals... Eventually we will have more property fenced properly so that there will be less chance of outside "pets" getting in. Until then, ?? I'm limbering up those shooting skills and re-learning how to fire distances... digging graves for other's animals - sucks in this weather and this day/age!
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Very glad to hear of OPs birds getting better and so sorry for your loss(s). I think it's a sad state of affairs when we aren't allowed to care for our own property and WE are threatened by someone who doesn't keep his own HOME.