No one wants litterbox problems, but they are common and occur for numerous different reasons. If your cat stops using the litterbox, the first thing you need to do is take the cat to the vet as there could be a medical problem contributing to the issue. Once the vet gives the cat medical clearance, then you can start to figure out why the cat is not using the litterbox, and when you know that, you can set about fixing the problem.
Some cats are very fussy about their litterbox and once used, may not use it again until it has been scooped. Some cats require two litterboxes, one for poo and one for pee. And yes, some cats refuse to share the litterbox with another cat. Even the litterbox itself can be an issue - some like it covered, some don't.
The actual litter can be very important to some cats too. Personally, I try to stay with unscented litter. Scented litter smells nice to us humans, but to cats, who have way more sensitive noses than we do, scented litter can be overpowering and distinctly unpleasant. The texture of the litter may also be important to your cat.
One of the most common reasons for a cat refusing to use it’s litterbox is that it is just plain dirty. Cats are very clean creatures and that includes their toileting. A dirty litterbox is almost a guarantee that your cat will find another location to do it’s business.
A general rule of thumb is one cat to one litterbox scooped once per day. If you have two cats, one litterbox may still be adequate, but it must be scooped twice per day. My two cats were happy with that setup for fifteen years until one cat became unwell - he made it very clear that he needed a second litterbox and even chose the location. Once a second litterbox was put in place, all was well.
Issues covered in this post are relatively easy to figure out and to remedy. Other, more complicated litterbox issues will be dealt with in a later post.