Apparently, it is fairly common because it comes up often on a web search. One of my twenty-four year-olds has taken to obsessively chewing on plastic. At her age, I am content with merely making a point of trying to keep plastic out of her reach, which isn't too hard, since she doesn't do a lot of climbing anymore.
As with people, the compulsion to chew on non-food items, such as dirt, electrical cords, and plastic, is known as pica. Some of the reasons suggested for this include dental disease or gastrointestinal disorders, so it wouldn't hurt to consult a veterinarian. Another reason is anxiety or the lack of stimulus in the environment, both of which I think may be at play in my cat. She has always been off her rocker. Despite the fact that she has been with me her whole life, she has always acted as if I was going to kill her if she encounters me anywhere other than in one of her cat beds. Sometimes, she acts like she doesn't even know who I am when she sees me in another room, and that's not just since she's gotten old.
As for chewing plastic though, while she used to be quite active, and a climber, at twenty-four, she has to consider whether she dares to jump down off of a chair, so I'm sure she misses the stimulus and security that she once got from being up high, and out of everyone's reach. I put shelves up on one wall of my office so that she could get up to the top of my bookcase by climbing from one shelf to another but, so far, she has considered it but hasn't ventured to do that yet. Of course, I had a large cat tree for six months before she would touch it.
Other sources of anxiety that could lead to pica might include a change in environment, a new cat, or other pet. One veterinarian compares chewing plastic to a person twirling their hair or biting their nails, as it's a coping mechanism. He also suggest that it might so simple as that it's just something that cat enjoys doing.
