Through the Veterans Administration veterans can receive pension payments to compensate some of the costs of assisted living, home care, or in some cases nursing homes. They are called the Household and Aid, and Attendance programs and they can pay well over half of monthly costs. Combined with social security benefits they could cover most of the costs.
You can obtain the documents for application from the VA and you will need to provide documentation that you have had at least 90 days of active service during a conflict, including Vietnam, with or without combat. You also need proof of an honorable or general discharge, excluding home your and car assets less than $80,000, and monthly medical costs exceeding your total monthly income from social security, pensions, or retirement plans. Assisted living falls under the definition of medical costs and easily will cost more than most seniors monthly income.
There are other veterans groups such as AMVETS, Disabled American Veterans or Veterans of Foreign Wars that are also equipped to help and are worth contacting as they may provide additional benefits.