Veterans Affairs Benefits. The Department of Veterans Affairs (VA) pays for long-term care services for service-related disabilities and for certain other eligible veterans, as well as other health programs such as nursing home care and at-home care for aging veterans with long-term care needs.he VA also pays for veterans who do not have service-related disabilities, but who are unable to pay for the cost of necessary care. Co-pays may apply depending on the veteran’s income level. The VA has two more programs to help veterans stay in their homes: