What is wrong with this hen?
I would give her a shallow bath to clean her vent feathers, and dry her thoroughly. Take another picture. She might just be having some loose poops, but she could be getting feather-picked or have something like vent gleet, which is a fungal infection of the GI tract. Many hens will get soiled feathers and need them cleaned off occasionally or need the feathers back there trimmed. Adding probiotics, probios powder, or some plain yogurt to the food a couple of days a week might help.