My state does indeed have a program for this, paying between $18-$20 per hour for what amounts to "assisted living" tasks, from laundry & cooking to home maintenance, cleaning, running errands, the whole shebang.
Their doctor just needs to write up a referral to have the state send somebody out to the house to evaluate them for eligibility (their doc is already leaning on them to let her do this for them anyway -- they just forgot to tell me), state approves the sorts of things they're "allowed" to get paid help with, I sign some paperwork, and then start sending statements every week or whatever. No waiting period, no application fees or anything, etc.
They've got an appointment already to see their doc about getting the ball rolling. The general stress level in the house has reduced by several orders of magnitude -- they've always "felt guilty" about me putting my career on hold and selling my house to come out to help them, and they worry about my finances but couldn't afford to help in that regard. My endless protests of "YOU'RE MY PARENTS FFS YOU DON'T HAVE TO PAY ME!" fall on deaf ears -- it's just who they are. They're over-the-moon at the prospect of the state chucking some cash my way for doing what I'm already doing.