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Inappropriate elimination is not an uncommon problem for cats and it can have various causes. You said that your cats are healthy, and that's great, but if they haven't had a recent urinalysis or fecal check, that would be a good first step. First, we would want to rule out any underlying medical cause for the soiling on your rugs, if they are experiencing discomfort upon elimination. This would cause them to associate the litterbox with the source of the discomfort and then, they would avoid it and eliminate somewhere else, usually a soft surface (carpet, rugs, bathmats, etc.) or a cook, hard, smooth surface, like a bathtub.
If this is a behavioral problem it could be attributed to any recent changes in the household that caused the cat to be frightened or feel stressed. If you have gotten any new furniture, did some renovations around the house, moved furniture, painted, had visitors (human and/or pet) or if there is construction outside, causing loud noises, these can all contribute to a cat beginning to eliminate inappropriately. If there has been a change in your normal routine with the hours you're at home, this could also cause stress. Stress is a major cause of soiling outside the litterbox.
Territorial marking can also be a cause of soiling around the house. If your cat is seeing/smelling strays or neighborhood cats outside your house, this can be a reason for marking, because cats communicate through their scents/waste and whichever cat is doing this is saying, 'STAY AWAY--THIS IS MINE!' If you know of any cats or other 'critters' hanging around your house, you can spray door frames on doors that lead to the outside, and also window frames, with Feliway (more info below) to help your cat feel 'this is my territory; I have already marked here.' Make sure to let dry for at least 30 minutes before allowing any cats access to sprayed areas.
A product called Feliway emits calming pheromones, only detected by cats and it comes in both a spray and plug in diffuser. The diffuser resembles a plug in air freshener, but has not scent. This has helped greatly, with inappropriate elimination problems. Here is more information:
Another important thing is to completely eradicate the stain/odor where your cat has soiled; this is so they can no longer smell their waste and then, think this is an appropriate toileting area. An enzyme-based cleaning product made just for pet/organic stains is the best type to use. Nature's Miracle, Zero Odor and Odor Mute are well-recommended and along with other products of this type, are available in your local pet supply stores and perhaps other stores, like Walmart, Target, and some home improvement stores. Follow directions on the product.
After you completely clean the soiled area, allow to dry and then lightly spray some Feliway over the spot. This will make the cat think that s/he has already 'marked' there. Very important: let the Feliway spray dry completely, as well, about 30 minutes, before allowing the cats access to the area.
If the rugs you referred to, are throw rugs, I would suggest throwing them away, if feasible and not getting any more for the time being.
Try to keep the areas being soiled, inaccessible to the cats, if at all possible, and lay down some sheets of aluminum foil or double-sided sticky tape, as cats hate the feel of these things under their paws and they need to scratch before and after they eliminate. While it might be unsightly, if it works to curb the behavior, it will be worth it.
Make sure you have at least 4 boxes, uncovered, in various places around the house. The ideal number of boxes is the number of cats plus one. If you don't have the room for that many, do what you can. If you have a multi-level house, make sure to have at least one box on each floor.
You can also add Cat Attract, a litter additive which contains herbal attractants to encourage use of the litterbox, to the cats' regular litter. You can find Cat Attract litter in any pet supply store or order online.
If nothing else works, I always like to leave the suggestion of a prescription medication as a last resort. There are many medications that your vet might suggest and I've found that Clomicalm works well. Here is more information:
I hope this was helpful and all will be well with your furkids!
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