We have one cat who shreds paper. It’s one of his methods of waking and annoying Master when he decides it’s time for breakfast. I haven’t seen any evidence that he eats it.
The other cat scares the bejesus out of us by not only tearing at, but actually eating, plastic. Fortunately, we were able to discern that this only happens when it’s in small ribbon form, so now we know to keep the jernt clear of all such material. Scary stuff, man.