Final answer:
Medicaid is the program that funds home care services for indigent and low-income people of all ages, covering medical expenses and nursing home care for approximately fifty million Americans.
Step-by-step explanation:
The program that pays for home care services to indigent and low-income people of all ages is called Medicaid. Established in 1965, Medicaid provides essential health-care coverage for around fifty million Americans, including the poor, disabled, and those over the age of 65, covering approximately half of their medical expenses with federal funding. The program is especially critical as it accounts for about two-thirds of the costs for nursing home care in the country. Each state has the autonomy to set its own eligibility standards, hence the extent of coverage may vary from one state to another. Medicaid, together with other safety net programs such as the Children's Health Insurance Program (CHIP), WIC, and Supplemental Security Income (SSI), forms a crucial part of the support system for Americans with low incomes.