The title covers the gist of it. The details:
We bought a new construction house in Central Illinois. The basement is mostly finished with a family room, bedroom and bath, but there is an unfinished section for the (covered) sump pump and HVAC/water heater. We have a 70-pint Frigidaire dehumidifier in there. The outer walls of the unfinished basement have sprayfoam insulation along the very top (above the studs), then pink fiberglass insulation between studs on the external walls - just to the frost line about four feet down (builders did minimum code).
We want to put a couple of litter boxes in the unfinished basement, but one of our cats is fully capable of climbing exposed studs (he's named Monkey for a reason!), plus there are storage tubs they could jump on.
We want to inexpensively cover the fiberglass to protect the cats without risking moisture/mold issues. We thought about using old bed sheets, but didn't know if that was safe.
I've read where people have used Tyvek (allows water vapor through, although I've seen disagreements on what side faces the insulation), fiberglass window screen or (too expensive for the area we need to cover) pegboard.