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How old is your cat?
Is he neutered?
Are the bowel movements normal, other than not in the litter box?
Thank you so much.
This is obviously a behavioral problem. First of all do not punish him by rubbing his nose in it and such. This Twill just make it worse.
I do not know where you keep the litter boxes, but you definatly need to keep one in the basement. Since that appears to be his place of choice.
You can use a litter called cat attract. Attract Litter is designed to make it easier to get cats of all ages trained or re-trained to use the litter box.
Very important to clean the areas that has been marked. You need to use a enzyme odor eliminating cleaner such as nature's miracle. Regular cleaner such as Lysol will not work as good. He keeps going to the same spots because he smells his scent there. You must get rid of the scent.
You can also use a product called feliway. This is a pheromone spray that helps cats with aggression, territorial issues, and anxiety. (Your cat is having a territorial issue.)
You can spray it on surfaces he has previously pooped on. Petsmart also sells it in a form called comfort zone. This is an electric plug in that puts it in the air.
When you do catch him using the litter box appropriately reward him with a yummy little kitty treat. Cats learn very fast a reward method of training.
As for the really bad smelling and soft poop, give him a tsp a day of plain yogurt. You'll be surprised how much this helps. It firms the stool and add good bacteria to the digestive tract.
Let me know if you need any other assistance.
All the products that I mentioned can be purchased at pet smart, petco, and most larger pet supply stores.