HiCustomerand thanks for your update and reply.
As long as you have not deleted the Trash from your Mac OS X Mail application,
the deleted files will actually sit in the Trash but are still accessible.
• All you need to do if you want to restore any Trashed email back to your inbox or another Mail folder you may have, is to simply drag the mail back into the inbox or that respective folder.
However, if the Trash in your Mac OS X Mail application for your Cox email account has been emptied, and the Trash is blank (no emails present) then that does mean your emails have been completely deleted.
Also,unfortunately the Tech you spoke with, would be correct in stating that your deleted mail is no longer accessible, because even though you are using Mac OS X Mail for your Cox email, this application is simply a conduit of sorts, to allow you to access your Cox account that your would otherwise have to access via a web browser, like Safari or Firefox for example.
What this means is that whether you empty trash from Mac OS X Mail or from the Cox website for the webmail, once you empty the Trash and not just delete the emails from the inbox, that removes the deleted emails from the servers of Cox.net.
So unless can retrieve the files on their side, there is no way to retrieve the emails I'm afraid.
My only recommendation at future preventive maintenance is to keep your deleted emails in the Trash as they are not really taking up a great deal of space, until you absolutely have to empty your Trash.
Believe me, I learned this the hard way myself, and so now, that is the way I process my trashed email, unless I am absolutely sure I need to empty the Trash.
Let me know if there are any other questions I can answer for you on this subject, as I am glad to assist.