Samuelson 1958 (pdf) built an overlapping generations model in which intrinsically worthless green bits of paper have positive value.
It is possible to build a mirror-image of Samuelson's model in which intrinsically worthless red bits of paper have negative value.
My model actually makes more sense. Because any infinitely-lived productive asset, like land [or Frances' cast-iron frying pans], could play the role of green "money" in Samuelson's model. But only a special liability, where free disposal is not permitted, could play the role of red "money" in my model. It's too easy to dump garbage in someone else's yard, but it's easy to keep records of who owns how much money. That's what banks do.
(I don't know if anyone else has already said this. I don't even know what this post is supposed to be about, except satisfying my own curiosity. But everything that is theoretically possible probably exists, or has existed, or will exist, somewhere.)