Medicare only covers medical care -- it doesn't pay anything for non-medical companion care. One of the only situations in which Medicare pays for any kind of non-medical care is when Medicare will cover home health care -- among other things, the care must be prescribed by a physician for someone requiring skilled nursing care, provided by a certified home health care agency, and only while the patient is recovering from an illness or injury.
when it provides short-term home health care, which is primarily nursing care but can include a small amount of help with the activities of daily living (ADLs) such as bathing, eating, and dressing. However, there are very strict rules about
If your parents have very low income and few assets other than their home, they might qualify for Medicaid, which is the state-administered program of medical coverage for people with little money. Medicaid's rules about home care are slightly more relaxed than Medicare's, and some Medicaid programs can directly pay the person needing care, who can then pay anyone they want to provide that care. But your parents would still have to require actual assistance at home to qualify for in-home Medicaid coverage -- Medicaid does not cover simple companion care.