My older sister lives with mom and takes care of her, but it is discomforting for her to always hear about the other's in the house at night or when she's away. My sis tries to explain in a nice way that no one else has been there, but mom keeps insisting.
Maybe I misunderstood what you wrote, but it sounds like you are saying your sister leaves her alone, maybe at night? Maybe Mom is afraid of being alone and could use a sitter for those times.
Or it could be a stage of Alzheimer's that your Mom is experiencing.