Can a child or other private person who cares for an elder parent get paid for 24 hour care?

Yes, if you get her on Medicaid LTC (in NYS), an unlicensed caregiver can sign up with the aide agency and get paid.

Where do you live? I've heard that in NY there are programs that will pay for around-the-clock home care. Other states use a Medicaid Waiver program to keep the person at home, but the total paid out generally can't exceed what it would cost to keep that person in a care center. (The cost of a Nursing Home in NY is $180,000/year -- more than twice the US average. So it is easy to see why NY has a huge incentive to have people cared for in their own homes.)

I don't know of 24/hour at-home care paid from from other public programs. Medicaid may provide for some additional in-home care for your mother (to give you some respite) or pay you for a certain number of hours. Generally this is at a rate close to minimum wage. It is a help, but it wouldn't exactly allow you to quit your job.

I think two sources you can contact for information about your specific area are the Area Agency on Aging (call Senior Help Line in some places), and also the regional office of an organization focusing on cancer such as American Cancer Society. If there are local options for help they would probably know about them.

Medicaid covers the cost of nursing home care for persons who meet their financial and medical criteria.

I am so sorry you are dealing with this.

Here is what the AARP website states:
Question: Can I Get Paid to Be a Caregiver For a Family Member?
Answer: In some cases and some places.
Your chances are best if you are caring for someone eligible for Medicaid and living in a state with a Medicaid care program or caring for a U.S. military veteran. But there are other possibilities.

Go to this AARP webpage for more information:
www.aarp.org/caregiving/financial-legal/info-2017/you-can-get-paid-as-a-family-caregiver.html?INTCMP=RDRCT-IC-CAREGIVING

I’m so sorry about your mom’s diagnoses. Unfortunately, caregivers who are family members seldom are compensated for our caregiving. If there is a government agency who will provide funding, it’s not very much. I found something through my local area Agency on Aging once that would pay $40 per week. They suggested taking out a reverse mortgage on our home, kind of like robbing Peter to pay Paul. If your mom has the funds, you can draw up an agreement that she would compensate you from those. I’m not sure though, if she is mentally incapacitated if anything she signed would be valid. I’ve never read here of any family caregiver who was ever subsidized to care for a loved one.