When did you deworm last time? If you didn't deworm them recently, I would try deworming first. Does she has water belly? does she breath normal? Before you try antibiotics, make sure the she doesn't crop issue first.
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Also, her poop looks like it has a bit of a yellowish goo tinge around the firmer bits.
This.Your hen likely has a chronic disease, and her feathers indicate she is probably at the tail end of it. I can't diagnose your hen, but she may have cancer tumors possibly cause by an avian virus.
I have lymphoid leucosis in my flock, and have had hens with deformed feathers and incomplete molts due to the tumors it causes. Not saying this is what your hen has, but when she dies, you would be wise to have a necropsy done by an animal testing lab.
You can try her on an antibiotic. Finding one over the counter these days is very difficult. If you have any leftover people prescriptions, you can use that.