This sounds like a simpler nurse aide level case. It is pretty common (from my experience at least) that some of these cases are just done casually and off the books. It is really like babysitting, except an elderly person instead of a child. A family will look for a friend/acquaintance who can sit with their elderly relative. Some families prefer this, instead of going through an agency, and having a total stranger come to their home.
Many years ago, I also helped out on a off the books nurse aide case. I basically just sat with the woman all evening - helped her to the bathroom when she needed to go, reminded her to take her meds, got a simple meal for her, did light housekeeping, etc. I actually know a group of nurse's aides locally who do cases on their own. They have some long term clients. It is all unofficial - meaning they don't have insurance, bonding, or anything like that... Both sides (the clients/families and the nurse aides) have the same understanding about it, and realize it is "casual" like babysitting.
Since you are a CNA (almost), and this sounds like a CNA level case - I really would not worry about much - expect to make sure you feel "comfortable" with the situation. Go to the home and meet the lady. Clarify what it is they expect you to do (that it is indeed just nurse aide type stuff). Clarify that pay would be cash and off the books. Etc. You don't have a nursing license to worry about losing or anything like that.
With RN (or LPN) level cases where the patient needs actual medical care and treatment, there are a lot more risks. Not only does a nurse have a license to lose, but things need to be more official for other reasons too.
I don't know what the "going" rate is for this type of thing, but the nurse aides I know locally who are doing this were charging $12 or so an hour.... that was about 3 years ago though. And this is the southeast, where pay can be lower.
Well, someone else may have a totally different opinion than me and tell you different!!! Anyone? But that is my two cents.