Chickens ae voracious feeders. At one time, I raised Cornish cross meat chickens, They weren't known as great egg layers, and were good sized birds. However, they supplied us with a steady supply of extra large eggs. And since we had roosters in the mix, we were able to use an incubator, and hatch them as well.
One time, I was gathering eggs, and feeding the birds corn feed. A large moues made the mistake of wandering into the coop. Those hens were on it in an instant, and had it devoured in seconds, literally. Chickens will eat hoppers, crickets, ants, beetles, ticks, mice, rats, grains, and starch water with abandon. They're like feathered pigs, true omnivores. The roosters even chased around two of my children, ages 4 and 2 at the time. But oh how that wild feed made the eggs so rich, and the meat so full of flavor.
So yes, chickens would have no problem with eating leftover chicken.
Seeeeya; Chief Longwind of the North