When Medicaid pays long-term nursing home costs for someone over age 55, Medicaid retains the right to be reimbursed -- after the person dies -- for the full amount it
spends for that person. As in your mother's case, Medicaid usually permits a person to keep a house until after death. But the house then usually becomes the asset out of which Medicaid is repaid. In other words, the Medicaid program does not allow someone to own a valuable asset like a house, have Medicaid pay for long-term care, and then let the family keep the house or sell it and keep the money.
In your family's case, Medicaid may have already placed a lien -- for the amount it spent to care for your mother -- on the property, giving it the right be repaid that amount whenever the house is sold. Even if Medicaid has not yet placed an actual lien on the property, you have been given notice by Medicaid that legally the family must repay Medicaid out of the proceeds from the sale of the house. Generally, Medicaid will wait for you to sell the house and then enforce the lien. However, if you take no action to sell the house, you (meaning you and any siblings who have shares in your mother's estate) must either repay Medicaid from other sources or eventually Medicaid will force a sale of the house.
How soon Medicaid will take steps to force the sale of the house depends on the state Medicaid program where the property is. Some states move more quickly than others. It may be many months before Medicaid gets around to forcing a sale, but eventually they will get around to it. If a long time passes between the time of your mother's death and repayment to Medicaid, your mother's estate may also be liable for interest payments on what is owed to Medicaid. It's probably wise to contact the state Medicaid program's estate recovery office to find out what their procedure is and how much time they will give you before you must sell the house or otherwise repay them.