Cats tend to groom themselves quite thoroughly, often helped out by their owners who brush away stray fur to prevent cats from vomiting up hair balls onto the carpet. Many cat owners may notice that their cat is losing fur around its rump and tail, and they don't know why. There may be a few explanations, but usually it's a grooming issue.
Generally speaking, if a cat is losing hair around their tail and rump it's because of overgrooming. This overgrooming (too many licks and bites to the area) is most often caused by skin irritation. The cat is attempting to scratch its itch, but it can't always reach down through the fur. So it keeps going until the fur eventually is gone.
One cause of the skin irritation that makes a cat groom themselves in this way is fleas. When a cat has fleas they bite the skin and drink the cat's blood. These flea bites cause skin irritation, which the cat will try to scratch, in addition to attempting to scratch and bite the fleas out of its coat. If you treat your cat with a flea bath and flea bomb your house, chances are good that the fleas will go away and your cat's coat can grow back.
Another potential cause of skin irritation for your cat that will make it groom off its fur are parasites, specifically ringworm. If you look at your cat's skin and you see raised bumps in a circle, chances are good that the cat has ringworm. In order to get rid of the ringworm you have to give your cat appropriate medicine that you can find at any pet store. Once the parasite is dead, the cat's skin can heal and the fur should grow back.
Another possible culprit for your cat's neurotic grooming and subsequent loss of fur could be mites that are located just beneath the skin. If you can take a small scraping of your cat's skin and take that scraping to your vet (if you don't take the entire cat) then your vet can likely find out whether mites are indeed present. With appropriate medication, the mites can be killed off and your cat's grooming patterns should revert to normal.
Visit the Vet
Regardless of what your cat may or may not have that's irritating their skin and making them lick away their fur, it's a good idea to visit your vet. Your cat may have multiple things wrong with it, and your vet can run all of the appropriate tests to be sure that your cat gets cured of everything and gets back on its feet.