House not in mother-in-law's name, can nursing home take a portion of the sale?

It depends on the state. Where I am, the transfer of ownership has to have happened more than 5 years before it's needed. So unless your state is different, the answer would be no. But a lot of nursing homes are predatory and will make you think that you're responsible for paying for a loved one's care. You're not (unless you agreed to).

Just a warning: if your LO has credit card debt when he or she dies, and you call the credit card company to let them know, DO NOT GIVE YOUR NAME. Just say, "this is her daughter." They can add your name to the account if you give it, and this has happened more than one person I know.

Who is on the deed and what name/s are on the taxes. And how long ago did Mom do this life estate. If 10 years the house is beyond the look back for Medicaid of 5 yrs. If her name is not on the deed or taxes, she does not own the house.

The NH takes nothing. If they except Medicaid, then Medicaid pays what they feel is reasonable towards Moms care. Moms Social Security and any Pension is used to offset her care. If she owns any part of the house, that would be an exempt asset. If her sons felt they needed to sell it then yes, Mom gets her % but that goes towards her care. Medicaid stops till she spends down the money and then reapply when its almost gone.

If sons choose to keep the house or can't sell before Moms passing, it will then become an asset and Medicaid (not the NH) will put a lien on Moms % of the house. Which someone can pay outright to keep the house or sell to satisfy the lien. Lets say Moms % is 40K of the sale but she owes 100k to Medicaid. Medicaid can only get the 40k.

Deeds are files at the County seat so no problem finding out who owns the house. If son's, then names will be on the tax bills too. You may end up having to use an estate lawyer to figure this out if its not cut and dry.

If it's not in her name, I don't know how anyone could assume it's hers. She's essentially a renter with a lifetime contract who bought a home for her sons.

How is the nursing home being paid? Is Medicaid involved?

Nursing homes don't take homes; Medicaid does estate recovery after the death of the elder owner.

You need a consult with a certified eldercare attorney.

From what you describe, she quitclaimed the house to her sons and has a life estate in the house, meaning that it’s hers with the right to live there until she passes. When she passes, they have joint ownership. So no, I don’t believe it’s possible for anyone to seize the home.

I don't believe so, if MIL's name is not listed on the deed. If she is on the deed it is possible. I believe you need a good attorney to advise.