Appointment letter, without any clause of separation, is incomplete one. Any employment contract shall have and must have a clause of separation -( mentioning end of service, by termination or resignation)
Please issue an addendum (giving reference no of Appointment letter) to all such employees who were issued Appointment letter, mentioning the clause of separation ( resignation or termination) and get it acknowledged by them on the copy of the same and keep it in file.
As regards to your query, you can regularise the issue by following the rules and procedure, as per certified Standing Orders of the company.