I was hoping to hear back from you, but I can send your answer now and then, if you have any other questions about this situation, please don't hesitate to ask.
It sounds, from your description, that your furry girl is very sensitive and timid. She seems to have had a difficult start in life, living in different shelters and elsewhere. I'm glad she ended up with you, in a loving, caring home! If she is sensitive, any slight change in her or your routine or environment may stress her and this may be why she began soiling outside the litterbox. However, first, it must be determined that this is not due to an underlying medical problem. Sometimes, cats who feel pain or have a problem defecating, will associate the place of elimination with this discomfort and choose to 'go' elsewhere. If her stools are not of normal color and/or consistency, she may have diarrhea, constipation or even intestinal parasites. A vet visit would be a good idea at this point, just to rule out anything medical and make sure this is purely a behavioral problem. If a medical cause is found, it will be treated.
Let's hope all is well, medically, and something stressed her and caused her to start defecating outside the litterbox. Cats are very sensitive to change and something that seems very minor to you (like changing the configuration of the furniture or having visitors) may cause her stress/anxiety. She also may be exhibiting litterbox aversion, due to the placement of the box. If it is in a well-trafficked area of the house, perhaps near a noisy appliance, this can be a deterrent to her using the box, as well, even though she had no problem with it in the past.
With 1 cat, you should have 2 boxes and they should be open, not covered, and use non-scented litter. You can use 'Cat Attract' litter in her entire box, or just add some to her current litter. As an alternative, you can buy 'Cat Attract' litter 'additive', which is a different product, and add that to her current litter. Make sure her boxes are scooped all the time and add new litter as needed. Once a month, empty it completely and wash in mild soap with warm water with some baking soda added to it. This will help to get rid of the odors that are trapped in the plastic of the box, but, as I'm sure you know, some will still remain. It's plastic, after all and a porous material. Still, monthly cleaning will help. Cat attract products are available in pet supply stores or can be ordered online.
To help with stress/anxiety and the inappropriate elimination, FELIWAY is a great product. It comes in both a plug-in diffuser and a spray; the plug-ins emit cat calming pheromones which have no scent to humans--only cats can detect it. Feliway is available in all major pet supply stores and you can also order online. Here is more information:
It's also possible that she smells some stray cats outside and is territorially marking, which is usually done with urine, but can be done with feces, as well; it's instinctive. If you do notice any strays or even a neighbor cat hanging around your house, spray the door frames of doors leading to the outside and also spray (with Feliway) the window frames/window sills inside, with it. You might also spray these areas outside, but, of course, if it rains, it will be washed away. When you spray inside, don't allow your cat access to the area for 30 minutes, until it's completely dry.
It's very important that you clean the areas where she soils, well, to remove all stains and odors so she doesn't return to the same places. Use an enzyme based cleaner like Nature's miracle, Zero Odor, Odor Mute or many others, available in your pet supply store and sometimes, Walmart carries these types of cleaners. After you clean, allow to dry and then spray a light mist of Feliway over the spot (again, allow to dry completely) and this will make her think she has already 'marked' there, so she won't return.
Try to keep things as calm as possible for her and when you find she has soiled outside the box, put her feces in the box and show her it's there--let her smell it and say gently, this is where you go poop-or whatever words you like. Leave it there for a day before scooping it.
When you get your additional litterbox (I'm assuming you only have 1 at this time), try placing it in the room next door to the one where her other box is, and where she is pooping; let's see if that makes a difference.
I hope you found my answer helpful and things will improve with your furry girl, soon!
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