If you provide room and occasional board for someone to 1) check vitals each morning 2) be there at night, 3) take to occasional doctor and hair appointments 4) some transportation, what would be the charge? The individual would have their own room and bath, access to use of pool, own refrigerator, etc. The parent does not need any assistance other than someone to ensure they take their vitals each morning (parent does know how), doesn't need medication assistance, cleaning, laundry, etc. Basically, the parent is fully independent other than requiring transportation as mentioned above. The home is quite large, pool, close to everything.
Your LO's home then becomes the primary residence of the roommate caregiver. This means if you wish to end/fire the caregiver you will need to legally get them out of the home, which may require eviction (a legal process that costs money and may take up to 30 days once the eviction form is posted). Also, a clever predator will know how to get your LO to make them the new PoA and insert themselves as an heir -- this happened in my family by a very "loverly" caregiver. Please just go into this with your eyes w-i-d-e- open. In the end this arrangement may seem convenient and "economical" but if it goes south, can be costlier than just hiring an agency vetted aid for a few hours per week.
You still need more than 1 caregiver. One person can not work 24/7 with no days off.
Typical for a "live in" is 8 hours "off" and a 3 to 5 day work week.
You still need to pay at least minimum wage.
Something as basic as this you could go through an agency and ask for "companion care"
You do not give any details in your profile.
If the parent needs no real care and mostly transportation to appointments or to the store UBER or LYFT would be much less expensive.