There can be two situations. First, where you get hospitalised before the policy expiry date and notify the insurance company before the policy lapses, and the policy lapses when you are still in the hospital. In the second situation, you may be hospitalised during the grace period, the policy lapses then, and you inform the insurance company about the same during the grace period. In both cases, the insurance company will compensate for the coverage availed, as per the terms and conditions stated in the policy document.