Posted to Tax for a better chnce of a good answer. Assuming your mother was getting Social Security retirement (not SSI), then the sale will have no impact on her receipt of Social Security benefits.
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A taxpayer can exclude form income up to $250,000.00 from the sale of a home owned and used by the taxpayer as a principal residence for at least 2of the 5 years before the sale. If teh home-sale gain is entirely excluded, the transaction is not required to be reported on a tax return.
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This is possibly excludable under Section 121 if your mother met certain residence requirements such as living in the home for two of the past five years. There are however somewhat more complex rules if you do not live there up until the time of sale as to what you can exclude. When you say "we" sold my mother's home, that makes a difference. The person claiming the exemption must both own the home and live in the home.
However, if she has not been paying taxes to begin with, that will not shield the other liability.