Yes. In fact, there are guaranteed acceptance permanent life insurance policies available for people between the ages of 50 to 85 years old.
Guaranteed issue means you cannot be denied coverage if you meet the age requirement for approval, can pay the premiums, and live in a state where the insurance company is licensed to do business, and offers the plan.
So, even if you have health issues, or you have been turned down for life insurance by other insurers, you may still be able to get insured.
Learn more about buying 50-85 year old life insurance coverage.