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.
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.