I'm sure they didn't have $1 plastic body scrubbers during The Great Depression, but if they did--and they completely unraveled--I'm sure they would have sewn them back together and kept on using them.
That's what I decided to do with our unraveled body scrubber, although it wasn't about the money. I just figured it would be super-easy to fix, and I might as well keep one more thing out of the landfill for as long as possible.
Surprisingly, it took about two minutes to gather back together and put a few stitches right through the center. I even made a new loop from which it can hang. Hooray!