Had a dog that chased the nearby farmers cattle. The farmer told us he could either shoot the dog or we could pay for the injured cattle. Dad told him to be sure to shoot the dog.
OTH. I hit and killed a dog with my car while it was running loose on the street. The owner thought to make me pay and was shocked to learn not only would he not be paid for the loss of his dog but he would have to pay for the damages to my car.
I had a similar experience. A dog ran out in front of my mother and was killed. The dog owner sought damages. I told him to claim against her insurance. They did and lost in court. The dog was lose and stray in violation of the local ordinance