This scenario occurs not infrequently at my home. I come back from work to discover a handful of cat litter on the carpet indicating where my dog, Pudge, has been snacking on kitty "nuggets" from the litter box. ARRGH!
Such a disgusting habit....right?! Come and get a "kiss" from mommy now. Not! Why does she do this?! The short answer is...BECAUSE IT TASTES GOOD! Really?! Believe it or not, cat poop is often higher in fat and protein and once a dog starts eating it, often initially attracted by the smell, they find it hard to stop. Does your dog have a nutritional issue? Probably not. If your dog is on a good quality food, they should have no need to seek out other sources of nutrition.
This issue has a fancy medical term, called COPROPHAGIA. It means eating poop, either one's own or another's (dog or cat). Although gross, it is a rather common behavior in the animal world. Occasional litter box "snacking" is probably not an issue, however regular or frequent meals could lead to parasite exposure (especially if your cat goes outdoors), and could interfere with your dog's normal digestion.
There are several techniques you can use to try and cheat your dog out of his snack. First of all, make sure you are scooping the litter box as frequently as possible to rid it of "opportunities". If you're gone a lot, a self-cleaning litter box may be a good option (see images on Amazon).
An alternative would be to try a COVERED LITTER BOX. In addition, a towel or "flap" can be placed over the entrance, still allowing your cat to do his business but discouraging your dog from sticking his head in. You can also place the opening of the litter box towards a corner, allowing your agile cat to utilize it while making access for you dog more difficult.
Another idea is to use a DOOR CHAIN to the room containing the litter box can allow it to open wide enough to let your cat in and out at the same time excluding your dog. This is probably, however, not a good idea if you own a Yorkie or a Chihuahua.
As a last ditch effort, there is a substance, called GLUTAMIC ACID, you can feed your cat which supposedly causes her feces to taste "bad" to your dog. It's worth a shot.