My cat does that all the time.But, he doesn't use the litter box for pooping. He's an outdoor cat. He sleeps in there sometimes. And, he bites me really hard if I try to get rid of it. So, I just give him a bath every now and then. I change it just in case, too. He watches me closely when I do.
Get her a covered litter pan, put a beanbag bed inside and let her sleep there. They seem to like the contact of the sides of the litter pan, as well as the feel of the litter on their belly. I have found the covered pan/beanbag to be a good substitute.