A common reason that people surrender their cat to a rescue is because their pet stopped using the box. Cat's prefer to use a litter box, they want to dig in the sand to use the box, this is their natural instinct. If a cat doesn't use a box, there is a reason. You have to be the detective and use trial-and-error to find out what the reason is they stopped using the box. Here are the most common reasons--start here:
They're sick. Most of the time, if your cat is going on the floor in obvious spots, they're telling you "Hey, I'm not feeling good." They can't speak English so this is their way of communicating with you! Your very first step if your cat has stopped using the litter box is to take them to the vet! They may have a UTI. After a round of medication, they'll use the box again!
They don't like the location. If your litter box is in a confined space, in a basement, near something loud (like a washing machine) or someplace dark. They might not want to use it because they're too scared to go there. If your litter box is in the basement, and they're on the third floor of your house, they may have trouble holding their bladder until they get all the way to the basement (especially if your cat is a kitten or elderly). Try putting your box someplace in the middle of your home (like the middle story) where it's quiet and isn't confined. Always remember that if you have multiple cats, you need multiple boxes!
They don't like the litter. If your litter is scented or makes a sound when it gets wet, they might not like it. They might not even like the way it feels on their feet (especially if your cat is declawed!) Try switching litters to an unscented litter, or a litter that is unlike the one you are using now. At Pet Angel, we use Pine Pellet Litter, and most of our cats like it! It works well for scent, the urine turns the pellets to pine dust, and you just scoop out the poop, replacing the entire box when most of the litter has turned to dust. If you have the crystal or scented litter, your cat most likely doesn't like it. Experiment with different litters to see what kind they do like!
Try a new litter box. If you have a covered litter box, take the cover off. They may be getting trapped in the litter box by another pet or young child. If you have an uncovered box, put a cover on it. They may not like how visible and out in the open they are when they use the box. If you have multiple cats, remember you need multiple boxes! Try to stay with a large box, your cat should be able to stand up, squat, and turn completely around in their litter box. If they're unable to do this in the box you have, it's too small and you need to get them a bigger one!
Clean the litter box more. Some cats won't use a litter box if it already is dirty. Make sure you scoop the box each day!
Move the box where your cat is going. If your cat is pooping in the corner of the basement, put a box there! They might just feel safe in that location, and not where the box is. By putting the box where they feel safe, they are more likely to use it!
If you tried all of these things, and your kitty is still going outside the box, give your vet a call for a follow up appointment. You can also look into a cat behavorist! They are wonderful at helping humans and their cats reconnect, and can easily help you solve the litter box problem so you can keep your kitty in your home! If your child was wetting the bed, you wouldn't rehome them, so don't give up on your kitty either!