I am truly sorry for your rooster. I have chickens as pets, both hens and roosters. The predators around us have gotten so bad we have to lock our birds up at night in their coops to keep them from being eaten alive. We try not to let them out until it's light. We've had to let them out (and not put them up) while still dark and have found one hen with her head missing, one hen totally gone and a hole in the side of the cage, and just recently we caught a racoon in the act of trying to eat the head of one of our roosters, who was protecting his girls. Brave little boy. His neck was broken so we had him euthanized. So I would think it may be hungry opposums, racoons and owls also eat the heads only. Too much building, not enough natural food for their population.
You people can go ahead and laugh but some people are bird people and enjoy them as pets. Some of my roosters are smarter than a few folks I personally know. And much braver and better providers. You could try putting out some live traps and catching and relocating the little fury troublemakers. We caught 3 in a row one week. No problems since. Also build a coop and put them up at night and lock the door. Just my opinion of course. Again, I'm one who is truly sorry for your loss.