Sleeping in Litterbox

We brought our cat home yesterday from the shelter and she has chosen to sleep in her litterbox. She was doing this in her cage at the shelter also. Also, she won't walk down the stairs. Her food is in the kitchen and the litterbox is upstairs. She is very friendlly and purring alot but not frisky or playful with any toys. she is friendly but hesitant. She was spayed 2 days ago but seems to be ok withit. She lets me pick her up. I'm a first time cat owner and need advice. She is about 9 months old. Thanks

It is quite common for cats (shelter cats and ferals) to sleep in litterboxes. Your best bet is to go out and buy several more boxes, so she can sleep in one, pee in one and poop in the other.

Give her time to get used to you. Don't expect to much out of her at first, she wants to be sure of you before she opens up. Maybe she just doesn't like stairs-she has been living in a cage for probably all of her life. So don't expect her to be to much of an explorer until she figures out you will only treat her with kindness and respect. Once she knows this, she will warm up to you and be a wonderful and loyal friend.

Thank you for rescuing her from a life in a cage.

Kitties often curl up in boxes, shelves, or any space just big enough for them to fit. She may just want to find her own cosy nitch in your home.
Her reluctance to climb the stairs is most likley due to her recent surgery. She should be limited in her activity as she has just had some major rearranging of her internal organs. Running, jumpiing, and chasing things should be limited. She will need rest and time to get used to her new surroundings.
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Like the others said. I'm sure she just needs time to adjust. I've seen many cats in shelters or ones that I bring him make a bed out of their litter box sometimes. I try to provide them with alternative things, another box with a towel in the bottom or a cat bed or a big dog pillow. My cats have this BIG purple dog pillow they lay on, and they love it. Some times just a pile of clothes is enough for a comfy bed for them.

I've had a few kittens and cats who didn't quiet know what to make of stairs when we first got them home, it would take them a few days to go up or down them.