When most term life insurance policies come to the end of the level term period (5, 10, 15 20, or 30 years), the life insurance company will require a much higher premium that goes up each and every every year if you want to keep the life insurance going. Due to this big increase in premiums, most term life owners let their life insurance policy expire at the end of the term.
Another option that many life insurance companies offer is the ability to "convert" your term life policy into a permanent life insurance policy without having to go through underwriting or prove your health. By converting to a permanent life insurance policy (at a higher premium) you will have lifetime coverage.