Destructive chewing is a common behavioral disorder of primarily dogs, and to a lesser extent cats. Pets may chew at walls, clothing, and bedding to name a few things. I have found that the most common cause of this in practice is some sort of nervousness or anxiety, often secondary to separation issues from the guardian. Other possibilities include some sort of nutritional deficiency, as well as metabolic problems or other systemic problems in pets.
Any pet with chronic behavioral issues such as destructive chewing should have a thorough physical exam, and possibly a complete workup at the veterinarian to include CBC/chemistry/thyroid blood tests as well as urine analysis. Any underlying medical diseases will need to be treated in order for the destructive behavior to resolve. For those cases primarily of behavioral origin, behavior modification training techniques, including graduated departures in cases of separation anxiety should be implemented and coordinated by a trainer or a veterinarian skilled in behavioral medicine. Natural calming agents including Be Serene and Composure may be helpful in some cases. In other cases prescription medications, including Prozac, Amitriptyline, or Clomipramine may be needed.