newbie to here

question

We have had cats for 30 years inside the house.
My question is sticky.
We have a white long very soft haired female that it around 10 months old.
Born in the wilds, caught at around the age of 6 weeks and then raised to date in the house.

This is the only cat that we have ever had that goes to the cat box, does her thing then sits down in her poo. She never covers it. It then gets in her long butt hair. We get home and its matted in, having to wash her each night.

We are thinking about shaving her butt, your thoughts on this or what?

What kind of litter are you using? I would not specifically shave her maybe clip her short. But she could be refusing to cover her stool because she dislikes the feel of the litter on her paws or the smell when she disturbs it; just about anything. Her sitting down in it makes me question if she has weakness in her hind legs; maybe a neurological problem? Od course she could be lazy. How does she react to the daily washing?