I was looking on this site for something to lock our bi-fold doors with (to keep Spooky out since he knows how to open them). I found something that is supposed to keep pets from unrolling the paper! One of the reviews said it helped with the scratching/shredding problem too, but I have never tried it so I don't know. We don't have this problem around here anymore, but I thought I'd share if you do!
http://www.kidsafeinc.com/product/48...per-Guard.html
http://www.kidsafeinc.com/product/48...per-Guard.html