H-1B status expires at the end of the employment period, regardless of the end date of the H-1B approval notice. There is no grace period to remain in the U.S. past that date so departments and employees should work closely together as the employment end date approaches.
Termination of the employment by the employer prior to the end of the H-1B petition validity period requires the employing department to offer to pay or pay reasonable costs of return transportation to the H-1B worker's last place of residence abroad.