Take the kitty to your vet to rule out a medical cause: parasite infestation, constipation, Irritable Bowel Syndrome, arthritis and others can all cause a kitty to poop outside the litter box. Some cats need prescription food to relieve cramping and pain or pain meds or supplements for arthritis. The vet may do an x-ray, fecal, or blood work.
Treat kitty for all parasites: worms (Pyrantel), Coccidia (Ponazuril) and Giardia (Panacur and Metronidazole). Some kitties don’t show signs of parasites but do indeed have them.
Look at the stool consistency. Is it normal? Too hard? Too soft? Does it have “things” in it like rug segments, blood, mucous or hair? What color is the stool? Stools that are too hard may mean that the kitty needs hairball remedy. Blood and mucous in the stool is not normal. Does the kitty have long hair? The kitty may need a trim around its anus to make defecating more comfortable.
Is there anything else going on with the kitty? Good appetite? Drinking well? Skin and coat normal or does the coat look dull? Any coughing? Normal activity?
Place the kitty in a small space (like a large 36”kennel) that is big enough for a litter box, food, water, and bedding to see if the kitty uses the litter box. If the kitty uses the box in a small space, give the kitty a larger space like a bathroom. While the kitty is confined, play with the kitty to help kitty be relaxed and comfortable.
If kitty does not use the litter box, first place a feliway collar on the kitty. Feliway is a feline pheromone which can help the kitty feel more relaxed and calm about using the litter box.
If still not using the litter box, then try different litters, different boxes and sizes and heights, covered or uncovered, multiple boxes, clean box multiple times a day, possibly different boxes with different litters. Litter comes in a variety of types: clay, scoopable, crystal, newspaper, wheat, corn, and pine.
Arthritic cats may like a box with a lower entry but high sides. Also avoid litter mats and strong cleansers. Litter box attractants like Dr Easley’s are also useful.
Look at environment and the location of the box. Are their bullies in the cat group? Is the kitty too scared to be stuck in a litter box pooping? Kitty may need a feliway plugin in the room.
Last but not least, the last resort is Prozac. While the kitty may be trying to communicate what’s wrong, the humans just aren’t understanding. Prozac for a couple months may help to level out the emotions of the kitty, especially kitties who have had the recent stress of losing their home or being in a shelter environment. Prozac is a prescription medication only available from your vet.