The best way to answer your question is to carefully read your health insurance contract to see if you are obligated to pay for the whole agreed upon term or if you can cancel it before the end of your term. Most policies allow the individual to cancel the policy before the end of the full term of the policy.You would be responsible for paying the carrier for unpaid premiums before cancellation. You most likely would be responsible for unpaid premiums before written cancellation of your health insurance policy.