Lilo the cat likes to eat fabric. Fortunately when she eats pillowcases, she tends to chew on the corners. Since most pillowcases are a little bit oversized, all I have to do is make a new seam at the inside edge of where she chewed:
I trim off the excess, turn inside out and – voila! – a perfectly fine-looking pillowcase.
(Of course, I can only repeat this process so many times before the case becomes too small to cover the pillow. That’s why I now store the pillows in a dresser when I’m not sleeping.)