@Hen Pen Jem has given a very thorough run-down. I would only add that there's a reasonable possibility that this very advanced bacterial infection has crawled up into her oviduct. If that has happened, you're looking at internal infection as well as the vent mess.
If this hen is not lethargic, isn't standing facing a wall with her tail down, has a good appetite, and as has already been pointed out - can poop normally in spite of the injury, there may be hope for her and it would be worth a shot at treatment.
If this hen is not lethargic, isn't standing facing a wall with her tail down, has a good appetite, and as has already been pointed out - can poop normally in spite of the injury, there may be hope for her and it would be worth a shot at treatment.