Financial question. Does anyone know how this works?

In principle, yes you can buy your grandmother's house - or, to look at it the other way, she is perfectly free to sell it. She would use the capital to pay assisted living fees; when the money is exhausted, and depending on what her income is, she will then be eligible for Medicaid. Provided you (or any other purchaser) had paid the full value of the house there wouldn't be any Medicaid penalty - she would have made no "gifts" to anyone.

But say, hypothetically, that grandmother gave you the house tomorrow, or sold it to you for one dollar. If she then lived at home for a further five years, and only after that needed an ALF, you could keep the house without grandma's incurring any Medicaid penalties if she were otherwise eligible. I'm not recommending this course of action, you understand, because it would be a cynical manipulation of public funding - not to mention a risk that elders with less scrupulous family members are sadly ill-advised in taking - but that's broadly how the lookback works. If she did this and then needed to move to Assisted Living next year, the value of the house would be looked on by Medicaid as a gift to you and penalties would apply.

As her caregiver you may have the right to remain in the home. Check your state requirements to qualify. A common Medicaid rule is if you provided care for a period of two years that kept grandma out of a nursing home (yes only nursing home, assisted living doesn't meet the qualifying criteria) then you can remain in the home after grandma moves.

If there could possibly be a significant difference between tax collector/ assessor value on the house and what it could be appraised at, I’d suggest that the owner (grannie) get an inspection of the house done AND THEN give that inspection report to an appraiser for them to do an appraisal. (I’m assuming that you’ve never bought a home b4 on you own, my answer is somewhat based on this)

Here’s why….
1. Often an elders property taxes are frozen, or limited in % increase annually, so taxes stay low even if the value placed by assessor/ collector increase. So if value increases in a big way over years but in actuality it’s not worth the higher tax assessor value, the elder doesn't care as taxes stay low.
2. often an elders property is old with decades of delayed maintenance.
But tax assessor value is determined by comps aka comparable value set by homes sold recently in the area that are same sq footage &/ or general description (3 BR, 2 BA). The recent sales will, I’ll bet, be places that are fully renovated, a flip, or a tear down/ new build. These are not truly “comps” to your grannies old house. They may be in the same zip code or maybe the same sq footage, lot size and maybe same BR / BA. But are not truly “comparable”, as these are homes r totally redone.
To find out exactly what the value is of an older home, you get an inspection & appraisal done. A good inspector will in detail find all the flaws, out of code issues w the house and with photos on their report which has their signature & state license. Appraiser then comes and does their own look, photos, Measurements, etc. and takes these plus the inspection report to do their own appraisal based on the specific property and not the comparables. It’s a legal document as it has their signature and licensing seal issued by the State.

If her place is old and last millennium for plumbing, electric, roof, etc., the appraisal will come in way less than a Realtors market value or tax assessor value. Could well be thousands less, or 50k, 75k less than tax assessor value. House (listed as “improvements” usually by tax assessor) could have super low value as it’s old & crappy and it would be more about the land value that the property taxes are based on.
You can buy the property for the appraised value as it is its true market value. Even if it’s significantly le$$.

Should you buy it from her, you should either be able to buy it in cash upfront in full at appraised value OR get a mortgage to buy it (so mortgage co pays her in full, title fully transfers and you pay a note ea mo to mortgage co). She should NOT do owner financing for the sale. If you did this, that payment to her will be income to her ea mo and likely take her over the Medicaid mo income limit (abt $2100). Plus her doing the lending gets into murky water on sale having “self-dealing” happening, which is problematic for Medicaid.

Whatever you do, please pls pls have a Real Estate attorney guide you both thru the paperwork needed to do a sale & title & recording done properly.

Also if u bought it, gran could pay you a modest rent for her to continue to live there.

You can purchase her home but it has to be Market Value. The proceeds are put away for her care. They can only be spent on her. No large gift giving.

I would have it assessed from top to bottom. Keep that assessment for your records in case Medicaid is needed at a later date. You should be able to purchase it at the assessment amount. You can check with Medicaid on that.

Medicaid is a state-run program, so the rules differ from state to state and that's why it's tricky to crowdsource your answer -- you may get an incorrect one from this global forum.

Generally, the house must be purchased for FMV (fair market value), so you must purchase it at the prevailing price of similar homes in her area. Then for sure you must have everything regarding the sale in writing and the way you pay her will matter so that Medicaid does not view it as "gifting". I strongly recommend you and she invest in a consultation with an elder law/estate planning attorney. It will be money well spent and you'll get answers to questions you didn't even know you had.