I have two cats, both sisters. We got them when they were kittens 2 years ago. They are both very timid cats, very skittish and they aren't really into socialising. One of the sisters has made massive improvement over the last 2 years, although very timid still she will let you pick her up and stroke her. She will now come sit on your lap for short periods. However, the moment we have guests, we don't see her for dust. The more timid of the two is worse, she will not let us pick her up or stroke her, unless we are sat in bed. She will follow me around but is always on edge. When we do get affection from her in bed she seems very content and purrs but sudden movement startles her. Neither of them will go outside independently. The back door has to be kept open, otherwise they will wail until they are back inside again. They've never left our garden.
We have a litter tray, they won't ask to go out and certainly won't do their business outside. The more confident one uses it without a problem. The timid one won't pee in it. We have had to put sheets and towels under the litter tray because she will pee on the towels around the outside of it, but not inside it. It is a large covered litter tray and is cleaned regularly. She will always poo in the tray though.
I'm not convinced they were very well socialised before we collected them, but we've built up trust with them both and they seem far more settled. I just don't have any solutions about the peeing. It's normally always the towels around the litter tray, although we can't put throws on the couch because she will mark her territory on those as well. She doesn't pee on the couch if there is no throw.
I'd just love some suggestions on how to make her feel more at home. She is a lovely cat but isn't really sure about life. Apart from being a little skittish and not very affectionate, she doesn't show many other anxious behaviours. She roams the house confidently, but she doesn't like change much. Any advice would be appreciated!