Notice Period and Company Policy
Notice Period will be as per the Terms of Appointment.
In this specific case, I understand that the employee is leaving the service without serving the notice period as per your Appointment Letter, which is OK/Fine with your company policy. By virtue of this, henceforth, if all employees decide to leave the service without serving notice, taking this case as a precedent, is it OK? As a special case, you can waive the serving of the Notice Period without it being regarded as a precedent.
Relieving Letter Details
In the Relieving Letter, you can mention being relieved with immediate effect, and the notice period as required under Clause # of the Appointment Order is waived as a special case, as requested by you.