I don't know what caused it, probably an untreated infection from a plucked tail feathers or infected oil gland... if she were mine I would get her cleaned up with a nice warm soak in an Epsom salt bath followed by a major trimming of butt feathers to reduced skin irritations caused by the poop build up, then coat her but with blu-KOTE and some triple antibiotic or petroleum jelly to reduce further sticking.
The diarrhea may be caused by the infection which you may be able to treat with a round of injectable penicillin. I would supplement her diet with some yogurt and scrambled eggs. She actually looks pretty good for general feather condition and alertness, so you are obviously feeding her well.
The Epsom salt soaks should reduced the build up around her sore and may loosen the scab. After each bath I would dry her off and put a good smear of triple antibiotic around the base of the scab, this will help avoid further scabbing and reduce new contamination to the area. Eventually you will need to get the scab size down so you can see what you are dealing with...and it probably won't be pretty but you would be amazed at chickens ability to heal. She is having trouble because her housing conditions were poor where she was at before so the contamination/infection got a foothold.
If she is friendly, and in good enough condition to lay regularly I would try to give her a chance. With some patience and cleaner environment she should show improvement.
And BTW, I never fail to be pleasantly surprised at how well our birds tolerate baths, they seem to actually relax during long soaks and ours even stand unrestrained for a blow dryer afterwards!