I used to tolerate loose single dogs wandering around my little farm until one day we came home from a day trip and I noticed a bunch of white spots in the pasture. They were 12 of our free-ranging chickens and one rooster, dead, just lying there.
It wasn't as if a fox or coyote grabbed a quick meal and ran off to feed on his kill, I doubt if I would have even noticed one missing bird. These kills were for sport.
After that, I would not allow a dog unaccompanied by a human on the property. I relied on the state regs on uncontrolled dogs harassing livestock.
It was S, S, and S from then on.