I don't even like dogs, but I would never kill one, especially if it belonged to a neighbor. It is really the neighbor's fault, not the dog's, although I understand the anger and frustration at repeated offenses. It's a difficult situation.
We had our first predator loss (I think, anyway) in more than 4 years. Crossbeak, our handicapped hen is the only one who flies over the fence and free-ranges everyday. She did not return this evening. We knew this would happen someday, although it is still sad. She was more of a pet and followed us around the yard while we tossed raspberries her way, so she had a good life. There was no sign of a struggle, so we suspect maybe a fox. I'm leaving the others locked up tomorrow in case whatever it was returns. I wish there was some way of knowing what happened....