It seems like you're actually asking about Medicaid coverage of long-term nursing home care, not Medicare nursing home coverage, which only covers short-term stays in a skilled nursing facility while a patient is recovering following a hospitalization. The Medicaid rules regarding income, including Social Security benefits, and eligibility for nursing home care vary somewhat from state to state because each state runs its own Medicaid program.
Your mother's Social Security income will be considered by Alabama Medicaid in two different ways. First, Medicaid considers it, along with most other sources of income, when deciding whether her total income is low enough for her to be eligible for Medicaid nursing home coverage. The Alabama Medicaid program's eligibility rules for nursing home care currently allow up $2,022 per month in income to qualify for nursing home care. If your mother's total income, including her Social Security benefits, is under that amount, she may qualify for Medicaid nursing home coverage in Alabama. (She also has to meet other requirements, including very low assets, and a need for the level of care provided by a nursing home.)
If your mother qualifies for Medicaid coverage of nursing home care in Alabama, most of her Social Security benefits will be paid directly to either the Medicaid program or to the nursing home, depending on how Alabama Medicaid sets up this payment system. She will only be allowed a very small monthly allowance for personal expenses (usually under $100) and for medical costs not covered by either Medicare or Medicaid.