Is there any program that offers free or low-cost senior dental care?

Medicare, the largest program of health care for seniors, doesn't provide any dental care. Neither do Medicare Advantage managed care plans or Medigap private supplemental health insurance plans.
Medicaid is the federal/state joint program of health care benefits for certain people, including seniors, who have low income and assets. It doesn't generally cover dental care, either. But a few state Medicaid programs provide some minimal dental care in certain counties. If you are enrolled in Medicaid, check with your local county social services office to see if any dental care is available to you through that program.

Another place to check is your county's dental association (the dentists' professional group). Some of these associations hold free dental clinics, or otherwise provide limited, low-cost dental care for low-income seniors. Also, if there is a school of dentistry – where new dentists are trained -- at a college or university near where you live, they may offer free or low-cost dental care at their clinic. Finally, check with local senior centers near where you live. They may have dentists who visit and provide free dental care, or they may provide a referral to dentists who offer low-cost care.