Is there any funding for someone who has to quit a job to take care of a parent who cannot be on her own?

Kathleen, majority of grown children who are caregivers for their parent do not get paid.... unless the parent can pay you out of their own retirement.

One option is to see if your parent qualifies for Medicaid [which is different from Medicare]. Medicaid is State run and paid for by the taxpayers. Depending on your State, there may or may not be a program that will pay you. If there is, please note the pay would be very minimal.