Can a nursing home take property that was donated?

Wills or codicils mean nothing when Medicaid is involved. Any assets the Medicaid recipient has after death will inventually go to Medicaid. First all bills have to be paid. Then tax liens and then Medicaid. If anything is left over, then the beneficiaries get it. Will and codicils are "just in case" you die. If you need to spend ur money before you die, no one inherits.

If this man has family or a State guardian, they may not be aware of this paperwork. Even so, if the property needs to be sold, oh well. If this document did not have witnesses and was not notarized it may not be legal. You need to see a lawyer.

The property was not donated unless your name was added to the title and the deed, and if this was done after admission to care on Medicaid, it would be a problem even then. The property, from what I can tell was bequeathed by will? And if so, before beneficiaries of a will get their shares, any creditor has a right to put in a claim for the remainders of the estate of one who died.
Medicaid will do first dibbies on clawing back likely.

Once all creditors are paid by the estate, then other beneficiaries of the remainder of the estate can put in a claim.

I am sorry you paid taxes on a property that wasn't yours. I think it may be lost.
Ultimately this is a law case, so do see an attorney with all facts in the case.
I wish you the best.

If the deed is still in his name it is his asset and can absolutely be a problem for him getting medicaid benefits and the state will be trying to get reimbursed with his assets.

Paying property taxes does not an owner make, not in 2 years.

Nursing homes do not "take" property. Even Medicaid doesn't literally take property. If your friend is on Medicaid when he passes, his property (or properties) will have liens on them as part of the Medicaid recovery program. You will have to clear the liens before inheriting the property.

As Beatty states, the property is not "donated" to you, even if you are a 501C3 (non-profit) organization -- it is bequeathed to the organization. You can't donate something (in legal terms) to an individual. This is called a gift. If your friend "gifts" you the property (in other words he signs the deed over to you with no money exchanged) then Medicaid would look at this as gifting and he may lose this financial benefit.

You, having paid the property taxes, means nothing in terms of ownership. If you do a little research online, in most states it never leads automatically to ownership.

If your friend wants you to have the property when he passes, he would need to create what qualifies as a legal Will in his state of residence. And he cannot be cognitively impaired when he does so.

Nursing homes do not take property, ever. When nursing home care is paid for by Medicaid, a government program for those in poverty situations, Medicaid has the right to attempt to get back or recover the money paid for that care. Your situation may well depend on the legality of the paper signed. Paying the property taxes has nothing to do with it. See a lawyer for reliable advice

"Donate his property to me when he died.."

This means you are a beneficiary in a will.. maybe not a legal will at that.

Whether a legal document or a scrap of paper, a will deals with how to disperse a person's assets (goods, money, shares, property) after they die.

You have no control over what they will have (or not have) at that time.

Assets may need to be spent or traded for care long before death.

Who is POA for your friend? That person would know how the NH is being paid - although would hold no obligation to share that info with you.

See if anyone can advise you here, but please seek your own professional legal advice.