Yes, you can still get coverage if you are diagnosed with a critical/terminal illness. However, the policy will be different. A policy, under those circumstances, is usually granted accelerated benefits, also referred to as living benefits, which allow the funds to pay out before the insured dies. Depending on the policy, a person can claim anywhere between 25 to 100 percent of the policy as early payment. However, you should note that receiving accelerated death benefits may affect your Medicaid eligibility.