Some varieties of cockroaches consider paper a delicacy or, on the opposite end, their preferred place for leaving waste. Envelope glue and just about any kind of paper attract roaches because of their smell and texture, and stacks of cardboard or food and beverage boxes are almost ideal places for hiding, eating and leaving trails of waste -- whether fecal matter or bacteria picked up on slender little feet and tacky underbellies.
Not only do cockroaches roll around in and feast on paper and cardboard products, they also destroy them with oils and acids that break down fibers and leave a really unpleasant smell. Keeping stacks of paper in tightly sealed cabinets and sorting rather than stacking mail in piles can help, as can disposing of cardboard outside of, but not too close to, the home as soon as boxes are emptied. Dusting recycling bins with a boric acid powder is not a bad idea either.