Actually, after TTing a looooot in one of my towns, I think there is a strategy. o:
As time passes, your villagers put their furniture in Retail. Buy it all so they can't buy it. Don't give them furniture or bugs or fish when they ask for it. I was originally doing this because I didn't want their houses getting cluttered with a lot of mismatched junk, and I noticed that their houses get very empty after a while, with only 3 pieces of furniture or so.
Somewhere around that point, my villagers started putting Sloppy furniture in Retail. Villagers that never had any Sloppy furniture in their houses to begin with, like Chief and Bam. They put it there pretty regularly, too, and more than one piece at a time can be in Retail at any given point. I probably have had two or three full sets of Sloppy furniture (minus the floor and wall, for whatever reason) pass through my hands because it was in Retail.
I think the game just has them sell Sloppy stuff (and a random assortment of other furniture that I'm positive they've never had in their houses) when they run out of actual things to sell.
Cardboard stuff is the same, but for whatever reason, I've only every gotten maybe 7 pieces of Cardboard furniture. o: Maybe it's different from town to town?