Yes, an annuity is like any other investment asset and must be liquidated and spent down before Medicaid will pick up the cost of your mother’s care. It may feel like the nursing home is “taking” the annuity, since it will likely be spent paying for your grandmother’s care, but in fact no one is actually taking it. Your grandmother will simply have to use the resource to pay for her care out-of-pocket. Once it is spent down, she will be eligible for Medicaid to take over the cost.
That said, your grandmother may be eligible for some ways to preserve at least some of the value of the annuity. We would recommend that your family consult with a local elder law attorney as soon as possible.