Had the same scenario a few years back on a piece of property. We always were seeing some stray dogs, and some big uns. A friend of mine and myself discussed what the ethical thing to do would be, and finally, one day during gun season, the dogs made the decision for us. My buddy was sitting on one greenfield and heard a heck of a ruckus with all types of whailing coming through the woods; he got down to investigate and found a pack of 4 dogs mauling a yearling deer. Safety off and dogpile em; one got away and came my way; I already knew what to do. Having somebody's pet come by with its collar on and wagging its tail can happen to any of us; a pack of dogs hunting deer wildly is another issue.