It is possible the cat is anemic- it is very common for anemic cats to eat litter, lick tile or concrete, etc. My cat almost died two months ago and that was one of the signs; I had to rush her to ER for two blood transfusions. There are other medical possibilities- I would go to the vet ASAP. I now use non-clay litter, as the clay can clump in their stomach and cause a fatal blockage. I use a clumping grass-based litter, and it's excellent! No dust either.