Nala ate her first bed like that! We got an outdoor one and she would lay on it and not chew it, but then my brilliant husband put it inside a wicker basket - she ate the basket. Now we have an enormous bed from Costco for inside during the winter and out on the porch during the summer.
We buy the beds like that at Wal-Mart for $10 so we can just toss them if she digs or chews them. So far, so good!
She's awfully cute!!