Permanent life insurance provides guaranteed lifetime protection to last your entire lifetime no matter how long you live.
Whereas, term life insurance which costs a lot less, provides temporary life insurance for a specific period of time, lasting up to 30 years, usually. With term life you may be able to choose life insurance for a duration of 5, 10, 15, 20, 25 or 30 years depending on your age and health.
Som, yes, term life insurance policies would expire if you outlive the duration of your term insurance policy's "term".
But, you may extend your term insurance for another term of up to 10 years (usually) if your policy offers renewable term life insurance.
If you renew your term policy your premium will increase at time of renewal based on your age at that time.