Cat eating her hair

Question
I moved almost 2 years ago. My female cat who was a little overweight suddenly lost weight. She then began chewing her hair on the sides of her belly. She constantly licks and chews the hair. I have taken her to two different vets and no one can give me answers. They did all sorts of tests on her. It's not mites, mange, of any other insect animal. One vet told me to change her food, and I did with no results. She was given a pill that was supposed to help her hair grow back fast but that had no results. I was also told it could be fleas, but they found no sign of fleas on her when I was told this. She has been an indoor cat until recently (she goes out to the screened in pool area now).

Another weird thing she does is she likes to chew shoes up. Flip flops, tennis shoes, etc she has chewed on the rubber pieces. It doesn't appear that she actually eats the chunks but leaves pieces all over the floor. Not sure if this would be related to the hair chewing thing.

Any help would be helpful. I'm at a loss at how to get her to stop. It makes her look horrible.

Answer
She could be allergic to something in the environment.  Ask your vet to try a shot of a long acting steroid called DepoMedrol.  This will stop any itching for about a month to 6 weeks.  If the cat stops this behavior, it is an allergy.  If it does not stop, then there may be a behavioral problem that may require a different type of drug, like Elavil or Prozac, to stop the behavior.