It may have been some sort of injury or attack that made the hole under her beak. I would try to get it cleaned up by bringing her in an either bathing her, or concentrate on just the gunky area under her beak. You will need to rub on it with a cloth or rag, and something like Hibiclens or plain dish soap would be good to clean it with. This may take a couple of tries with another pair of hands helping to hold. Once it is cleaned up and debrided, take another picture or two, and apply some plain antibiotic ointment. Chickens have suffered tongue injuries in some past threads, and could eat without a tongue. I hope that she makes it.