OMG, what a cute picture. "Must shred box, then sleep in it..."... I can just see his determination on that one!
My cats don't destroy or chew the boxes. Snickers keeps them intact because he uses them as a fort, as a hiding place, so as to attack Hammie or Dusty as they walk by. I have a box in each room now for him, but it certainly doesn't get destroyed!
Plastic bags are another story however. Hammie just loves plastic and I have to be very careful with him about that. And Zorro licks curtains. He bites them on occasion and leaves little teethmarks, but mostly, licks them!