My cat has stopped using the litter box. Consult your veterinarian immediately. If the problem is behavioral, the litter box may not be clean enough for the cat. Feces and urine spots should be removed daily. It's a good idea to have one litter box available per cat.
Most cats use commercially available litter without any problem.
It won't scratch the litter or cover up its stools when it defecates. It may shake the litter from its paws or stand on the edge of the box to avoid getting its paws in the litter. Rather than digging in the litter when it uses the box, it will scratch on the sides of the box, the floor, or the wall. If the problem started when you switched brands, revert to the original one. If you've switched from non-deodorized clay to a deodorized one, this may have bothered the cat.