Why are there always spiders in the litter box?

I clean my cat boxes just about every day, but at least once a week I stir up a spider in there. Different types and sizes, but there always seems to be a spider buried in the litter box… and alive. It’s not like we have flies or other bugs, which might make sense. I’m fairly certain that spiders don’t eat poo… so why are they hiding in the litter boxes?
As if they aren’t gross enough, adding spiders to the equation seems like overkill. :\