She maintains the house out of love: In the live-action movie, Cinderella (Lily James) starts taking care of the house not so much because of her stepmother's orders, but because her stepmother has fired the house staff and she hopes to preserve what her parents loved.
She stays to preserve her parents' memories: Along with a lack of options, it's also her special family memories that keep Cinderella at home. After all, in the new movie, she does head into the woods and go into town, where she runs into a former member of the house staff, telling her she's stayed to look after the home her parents built.