The delivery period runs from first-notice-day to last notice day, typically a few business days after last-trading-day. Anyone still short after the last trading day must deliver within that window; anyone still long must be ready to receive.
Because trading has already stopped, there is no way out except by finding a counterparty in the physical market or paying the exchange's alternative delivery procedure fees.
Example: in many grain contracts the last notice day is the second business day after the last trading day, so a short who forgot to close has roughly 48 hours to arrange 5,000 bushels of deliverable wheat at a registered elevator.
Related: first-notice-day, delivery-notice, last-trading-day, physical-delivery, spot-month