this problem is new to me
It's really hard to tell in the photo what I'm looking at, but as per your description, it sounds like she has either vent gleet or possibly an infected vent from egg binding or a worm or mite infestation.
Does she walk normally? Or like a penguin?
Was she very messy with runny smelly poop and red swollen vent (vent gleet)?
Or just really runny messy from diarrhea (worms)?
Could she be infested with mites, which can cause a lot of skin irritation and feather loss at the vent?
Check for those things to see if maybe one of those is the answer.