I thought I was being clever, putting the litter box on wheels so I could slide it out from under the stairs, but I have inadvertently created a Mad Max-esque vehicle which my cat uses to roll around the house, dragging himself with his front paws, the entire time shitting.
We put our cats litter box in the basement. We had this wicker box thing down there. It’s kind of small, like a little box that could hold 6 pairs of shoes. It was near the litter box and she drug it over to her litter box so she could scratch at it while she took shits. We wanted to stop her from destroying it so we moved it far away, she drug it across the basement back to the litter box, twice. We put weight in it, she knocked it over and then moved the now empty box back.
We gave up. It was like $10 and we obviously weren’t using it. It’s hers now. She has wrecked it. It’s like a boomer dad taking a newspaper into the bathroom. We find chunks of wicker in her litter box. The front of the box is bare. For the record she is not an especially large cat, she is 14-15lbs
I mean, it's at least plausible. Cats scratch the sand before and after using it, to cover their tracks, and while they can be incredibly smart when they want to they can also simultaneously be astoundingly stupid... so they sometimes scratch outside the sandbox.
If they do that on a sandbox with wheels, it's not out of the question for them to move it (especially if they can sink their claws into something, like carpet).
That gives you two possible scenarios for the story: the stupid wins, and the cat is just trying to cover its business but is moving the sandbox instead, or the smart wins, and the cat figures out it can move the sandbox wherever it wants, which will probably be near its humans, as cats prefer to have someone nearby watching for predators while they do their business.