Archived tickets are tickets that are automatically closed after 120 days of inactivity. These can not be reopened.
The traditional APIs (whether “get list” or “search”) never return archived tickets.
Freshdesk introduced some APIs for archived tickets, but as far as known these APIs do not provide a list-like interface. An archived ticket can only be retrieved by it’s ID. See:
https://developer.freshdesk.com/api/#archive_tickets
Since these tickets are not practical usable and do not allow retrieval of all archived tickets in any efficient way, archived ticket APIs have not been included.
An alternative would be to use the new export API (asynchroneous), but that one is currently not included since it is async.
Maybe Freshdesk Support can recommend an alternative approach or an undocumented API to retrieve the list of archived tickets.