In PDN i got this statement "Deletion of an Operator ID instance is not allowed when there are open assignments on that operator's worklist, or when that Operator ID is referenced in another data instance (such as an organization unit or workbasket)."
If it is deleted what about that work objects or open assignments in that operator's work list.
I believe the work objects won't be deleted as a result of operator rule's deletion. You can check corresponding pc_work table for your case. To work on the open work objects created, one has to reassign them to the available operator.
It can't be possible to delete the operator and eventually it deletes the credentials from LDAP, if it is really happening in your case then this could be serious issue.
By any chance if you delete the operator and relogin with LDAP username/password then if you are calling 'EstablishOperator' activity from your authentication activity defined in authentication service rule would create the operator again, provided that you should add basic information to create the operator such as 'access group,Organization[name,div,unit]' etc.