Rabbits are the most natural prey for wolves. Dogs chase them being driven by sheer instinct, as well as they have a habbit of digging the ground - because mice are their natural prey as well. But I don't think that it was your dog, because you would hear him barking prior to killing. He, without any experience, would only injure the rabbit. It wasn't a coyote or a big cat, because the rabbit wasn't even partly eaten. Most likely it was another dog, experienced in hunting and killing them. His owner left the body for wildlife to eat healthy food, or to poison some wildlife representatives.