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If your mother receives social security benefits based on her earning records and Medicare based on her age - these benefits will not be affected.
However - if she receive Supplemental security Income (SSI) and Medicaid which are need based - these benefits might be affected.
If she wants to give her property to her son while she is alive - that is a gift and not inheritance. Her gift is equal to the fair market value of the property minus the mortgage balance her son is willing to assume.
The issue that she will face when the time comes to apply for Medicaid (Title 19) benefits or any other need based benefits. Technically, all of the applicant's countable resources should be used to pay for these benefits. Any gift made within five years of the application will create an automatic period of Medicaid ineligibility based on the amount of the gift.Federal law requires each state to have Medicaid recover program and a lien will put on the property. If the property will be sold - part of proceeds owned by your mother should be remitted to Medicaid.
If the amount she will continue to use the property as her primary residence - her benefits should not be affected - but the state will put a lien on the property for at least five years.
If she moved out of property before five years - the property will be ceased by the state.
In additional - a fair market rental value will be considered as her income provided by her son - and that might affect her SSI amount.