My partner and his brother have laying hens. A common weasel that lives in the wood shed, took two of the chickens out today. There has to be better uses for these chicken carcasses than to throw them in the bush, which, although a natural thing, to me it feels like such a waste of materials, but is exactly what they'll do. I suggested to turn it into cat food. Would love to read other permies' suggestions for what to do with dead chickens.
You could consider skinning and cooking the meat to feed back to the remaining birds or to feed your dogs. They need protein, meat is protein.
Using it a bait to trap the predators is a good idea, if you are so inclined.
Aside from those two options I don't know what to suggest.
If your compost pile is large enough to be hot you can compost them.
Feathers can be used for crafting.
Untouched meat can be cut away and eaten if it's cold enough. Where I live right now it's colder outside than in my fridge so it'd be OK for a day easy. So if they gnaw through the chest but leave the legs untouched the meat might be OK, just a little dark (good for soup!).
You can clean the bones for crafts or display.
You can debone it and bake the bones 'til they are able to be broken with your fingers and feed them back to the chickens as a calcium supplement or use them as bonemeal in your gardens.
Hello, please call me Mouse. Talk to me about rabbits, chickens, and gardens. Starting an intentional community in Ohio.