Posting for my mom

8 year old Barred Rock. We found her still perched on the roosting bar this afternoon. My daughter went to check on her and she flew down then wobbled then loafed like this. I checked her legs and her feet they look fine. But I did discover she has pasty butt and is missing some feathers on her back side above her vent. She's still laying eggs, dining and eating. Isolated and does have a stinky smelling poop. What could this be and how do I treat it? I don't want to lose her she was my first chicken I got with my original flock. Her name is Poppy.