Do any of you caregivers whom do this for a living, ever care for anyone who goes into the hospital?

who goes into the hospital and he/she still wants you to be there everyday, and then they go into rehabilitation, and want you everyday, because they feel that with you around, they are not lonely, have someone to talk to, and have someone to tell them to keep going? Is this normal, as I have a woman that is very lonely and is 72 years young, and has been hospitalize several times since I have been with her for 2 years, she insists, every time that she is in the hospital, that I not leave. She is a widow, and her girls and boys live in New York, Pittsburgh, Delaware. She has some relatives here California, but not close to them.
She has the finances to fund this kind of care, and I am forever grateful, and do give some of the monies to charities to do my part. Are there many jobs out there like this? I feel so grateful, but want to be as open and honest with her, that it is ok, if she doesn't need me. My husband and I have talked with many people about her and our situation, and they feel that she is very lonely, and uses me as not only her care giver, because I do work very hard every time I am with her, in her house or not. She does need me in an emotional way. She is a tough woman, but underneath she is quiet as a mouse, and her feelings get hut very very often. Hoping that this is normal for some care giving people. I know that each job is very very different, and that is so true. Any similarities, it would be great to hear!!!! Thanks.