The nursing home cannot go after the money given as a gift. However, to the extent that Illinois Medicaid funds are needed to pay for your nursing home care, your eligibility for these funds can be reduced by the amount of transfers of non exempt assets for less than fair market value during the previous three years.
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I have read Mr. Kreisler's answer and I would agree with him. His answer gets right to the point.
However, he also states that it is important to know all of your circumstances to give an accurate answer. It depends on how much you have gifted away, when you made the gifts(s) and how long it will be until you will entry a nursing home (and need to apply for Public Aid to pay for your care).
I would suggest that you look at the website naela.com to find an elder law attorney in the Pekin area. He or she would be able to help you.
In addition to the answers above, I would add that Medicaid transfer and penalty rules are very complex and uncertain in Illinois at this time. I would speak specificly with an elder law attorney in your area using the website Paul recommended. When you see the elder law attorney, I would ask him or her how to structure your gifts so that you can fall under a specific exception t the Medicaid transfer of value rules that permit gifts that are not in contemplation of accelerating Medicaid eligibility. I stress again how incredibly important it is to get competent and accurate advice on this before you do anything since the consequences of doing the wrong things can be quite catastrophic.