Is their litter clean?
cats
A place to talk about and post pictures of cats
In addition to the clean litter box and marking of territory, my cat used to shit on my bed due to separation anxiety if I was gone for more than a night or so. The only way I stopped it was keeping my bedroom door shut. When I travel now I’ll fold up the comforter and put it in my living room so he can still sleep on something that smells like me, and he’s chill, and he has yet to shit on the comforter. It’s just something about the bed idk.
I’ll strongly voice my support for the suggestion to take your cat to the vet though.
Cats can have a wide range of reasons for relieving themselves outside of the litter box, so it's hard to say for sure. It's possible that the cat is trying to mark its territory, or it may simply be because the litter box is too dirty and the cat doesn't want to use it. Have you taken your cat to the vet recently? They may be able to offer more insight into your cat's behavior.
does your cat use the litter box as well, or is it just on the bed?
That sounds like a stressed cat to me. Perhaps a visit to the vet may be the correct choice