She's stay hiden for days sometimes, and wouldn't come out to eat or use the litter box (she'd just hold it), and not eating or pottying is really not good for cats
I see, yes, it is important for them to eat and eliminate, for sure.
I've had Brutus, a male neutered basenji, for about four years now. I got him from a shelter and they told me he had been returned by two or three other families. He was pretty rambunctious when I got him (he ate a couch once!) but he has become a pretty good dog except for one issue: He keeps peeing in the house. Everything I have read says I need to catch him in the act in order to train him, but I have never caught him in the act. He is very stealthy and only does the deed when not being observed. I tried crating him when I first got him but I could not get him in the crate, nothing worked. And he peed all over the crate as soon as I wasn't looking. He's gotten better and pees less than he used to but I really need him to stop peeing totally. Does anyone have any suggestions?
Try tethering him to you so you know where he is and what he is doing. If he tries peeing tell him "no" and take him outside immediately. There is usually a pattern for when they need to go, as in, first thing in the morning and after meals, but take him outside regularly and praise if he pees. Does he lift his leg or squat? Bottom line, you do need to be more observant until you get this problem sorted. Crating or confining in a small area usually helps, but if he is crate averse that isn't a solution.
I should have mentioned that he has a dog door into the back yard that he uses regularly. So he can go out when he wants to. He has never pooped in the house. I don't think he is peeing because he has to pee, he's responding to some issue he has. For example, if the area by my front door is clear he won't pee there, but if I leave a package or something else there, he will pee on it, like he doesn't like there to be any clutter.
if I leave a package or something else there, he will pee on it, like he doesn't like there to be any clutter.
O.K. that gives you an opportunity to "set him up" so you are able to correct his behaviour. Deliberately leave something there, be nonchalant but keep an eye on him, and if possible catch him in the act. This sounds to me like some sort of territorial response.
For what it's worth, I have never bought into the theory that you actually do have to catch them in the act to correct behaviour. I base my opinion on having trained two farm dogs not to defecate or urinate in my barn, despite never having caught either of them "in the act". Expressing my disgust in no uncertain terms upon finding the evidence resulted in the behaviour ceasing in short order. One of my barn trained dogs went to a new home with my sister, where he never disgraced himself in the house, so the behaviour was generalized to indoors.
I'm starting to feel like I solve all problems with a walk.... BUT! Take him for a walk. A long one. When he "waters the grass", praise him. "Oh! What a good boy!" (Please do not reach down and pet your dog while they are peeing. Yes, I've seen people do this.) Just use your voice and facial expressions to show how proud you are of your dog doing it outside. Then make daily walks a "thing".
FWIW: I agree with @eeeefarm. It sounds like your boy is marking his territory. Perhaps Brutus is expressing anxiety over being bounced from home to home. No doubt his other families rejected him over this specific behavioral issue.
For a temporary reprieve from all the stealthy peeing you could use a belly band on him. I order mine from Sew Dog (www.sewdog.com or https://www.etsy.com/shop/SewDogStudio) where they are made to measure. If you go this route order the custom insert pads. I found if I used disposable sanitary type pads my dogs would tear them up and consume them.
What worked for me was taking my Basenji for a short walk along the road that I live on every hour until she went. After just a couple of days it made a big difference and after that I increased it to 2 hourly, 3 hourly and so on. I think it worked because she became used to going outside and it felt less familiar going inside. Going outside and waiting for her to perform with her getting stressed, wanting to go back inside and not understanding what I was asking didn't get us anywhere and this was much quicker and long lasting. Now she goes for 2 decent walks per day (morning and night) and usually asks to go into the garden once in between (she is 18 months old). My Basenji was a puppy so if you decide to try this you may not want to start at hourly. The other benefit of this is that she doesn't tend to want to poo in the garden unless she has an upset stomach.