Unlike dogs, who can often be caught in the act of gnawing on sticks, interesting-smelling articles of clothing or your favorite pair of shoes—cats are typically pretty savvy about knowing what they should—and shouldn't—eat. So pay attention when your feline starts snacking on stuff that isn't food. Sometimes it signals a bigger issue.
Bring your cat in for a vet check if you notice sudden changes in appetite or preferences. For example, an increase in appetite may be a sign of hyperthyroidism in older cats. And eating litter may be a sign of anemia.
Cats can have compulsive disorders, where they eat things other than their food or groom obsessively, which causes skin problems. If you notice any unusual new food preferences (or a taste for non-food items) or bald spots on your cat, seek out a board-certified veterinary behaviorist to see if your cat is trying to signal some kind of stressor in its life.
Siamese or Birman purebreds are more likely than mixed-breed cats to suck and chew on wool. This can be a serious problem—eating strings could tangle your cat's intestines. If you have a cat that seeks out wool or other strings, do your best to elimate them from your home. Also check any cat toys you already own for any strings or threads with the potential to unravel while your cat plays with them.
Indoor cats may eat odd things for entertainment, such as shoelaces, ribbons and tinsel. Offering toys, games and playtime can help. You can also buy puzzle-like toys that release food when your cat correctly figures out how to move or agitate the toy to dispense a few kibbles to munch on.