It is the responsibility of the employer to notify the ATO when an employee ceases employment. It does not matter if the employee is terminated or they voluntarily resign.
When the employee receives their last payment, you are required to give the Cessation reason and date. This will then be reported in the next Pay Event sent to the ATO.
At the time of sending the Pay Event, you can tick Final Pay, or you can select Mark All as Final in bulk at the End of Financial Year, when sending STP Update.
By ticking Final Pay you are advising the ATO that you will no longer be paying this employee in the current financial year. If you have an employee who is permanently leaving the country and is required to do their tax return, you will need to tick Final Pay in the next pay event.
For more information, check the Australian Taxation Office for reporting requirements when an employee transfers or leaves.