Hi,
Without being able to catch this cat there's not anything you can do for her. There are a wide variety of possible problems going on with it, and no way to know which it is. It could be anything from a severe flea infestation, hyperthyroidism, skin mites, having been exposed to something toxic, to bacterial infection and more. Here is a link to a page with a chart of skin conditions in cats:
http://www.peteducation.com/article.cfm?c=1+2141&aid=202
If you have further questions let me know. If this answers your question please click accept. Thank you.
Lynn
Veterinary Assistant
worked at a vet clinic for 15 yrs, BA in biology, have had cats most of my life