Does you cat eat fish? You may be surprised to learn that lots of cats are allergic to fish, and the allergy may just start out of the blue.
I've had 2 cats who were allergic to fish. One of them I adopted as a stray, so he may have always been allergic, but the other cat I'd had since she was a kitten and she had always eaten canned and fresh fish, along with her other food. All of sudden, when she was probably around 4-5 years old she started to develop scabs like you described, around her tail and on the side of her face. People didn't want to touch her because she looked diseased.
The vet ruled out fleas, but said it was possible it was fish and told me to eliminate it totally to see what happened. Sure enough, the scabs cleared up, but to be really certain I started giving her fish again and the scabs came back. So fish was totally off the menu. After a while I found that I could get away with giving her fish maybe once a week without any problems, but I have naturally avoided fish for all the cats I've had since her. In fact the cats I have now actually really dislike fish, so that solves that problem..lol...