If I know that it is a neighbors pet then I would warn the neighbor first but where we live there are a lot of strays dropped off. I have to neighbors that rescues all the dogs they can. Both of them has so many dogs its unbelievable. Two different time cats has shown up at our house but something laid their stomachs open and killed them or I probably would have kept them. I don't know if it was a coyote, pig or what the heck it was. They were both near one of our ponds.
If it was a neighbors cat they did not warn me before it killed 4 turkeys, 2 chicks and ate 8 turkey eggs a day before they hatched..
I shall give the neighbor the same warning....BTW I do not have a close neighbor, or particularly care for those closest to me.