If you lost half your own arm in a car wreck; You would be in shock and depressed. But after a while you would eat. I am sure you would have pain. A bone sticking out without treatment will become infected. You would become septic, feel real bad, run a fever and eventually die.
Now if you saw a doctor he could remove the bone back behind the soft tissue, maybe even pull some muscle over the bone stump and stich it. then pull some skin over that and stich it. Treat you with some heavy duty antibiotics to prevent infection. In time you would use that stump, and live a productive life.
Damn the Opossum and his apposable thumb. He can reach right through the wire grab one of your girls and pull enough through to eat a whole wing off. That thumb and his tenacity allowed him to continue as a specie to today and beyond. But this wasnt so good for your friend. You have some choices to make.
After death there is no pain
making no choice most likely means infection misery and a slow death. Now it could become a local infection and rot enough tissue for that bone to fall away, but dont count on it.
A vet will probably charge you a little less because it is a chicken. Probably reach in there snip that bone at the joint, stich muscle and skin together in a few stiches and give a heavy duty shot of anti biotic + maybe some thing you can add to the water.
$40 to $60.
I have learned that chickens are not just dumb egg producing animals. Most of us back yard people enjoy our chickens for more than meat or eggs. They are our pets. They often inspire us to see the world in a different perspective. Good luck in your choice.