[Soliloquy]

Cats may think they can go in anything they can dig in. Which is why they go for baskets of laundry and un-made beds. Making the beds every morning will probably help (I know, more work!).

If the cats were previously outside cats or in-and-out cats you might not be able to stop it. They may need to be outside.

I have a cat that likes to sleep in baskets of clean laundry so I put another basket on top of that basket, if I can't fold and put it away immediately.

Cats hate the feel of aluminum foil under their feet. They also hate sticky tape. So, if you know it's not a health problem, putting sheets of aluminum foil or circles of duct tape on the areas may teach them to avoid it. Cats also strongly dislike citrus so some essential oils (lemon, orange, etc) may discourage them from those areas.

I second asking the previous family what kind of cat litter they used. I've never had a cat that cared but some do. I really like the pine litter. It's also sold in bigger bags as horse bedding (wood pellets).