The emails are essentially permanently gone from AOL's servers. There is no way to contact AOL to retrieve them.
If they had AOL setup within Microsoft Outlook, Windows Live Mail, or something similar at one time. They may have had AOL setup with a pop3 account which downloads emails from AOL servers to their computer locally, which then removes them from the servers as well. So without the emails saved locally on a computer somewhere they can't be recovered.
If you have a way to contact AOL, it's worth a try. I would say the chances they have a backup dating 6+ years is unlikely. Usually places like this has a policy of how long they keep a backup for certain things. Email is not going to be high on the list, they probably only have a record dating back a couple months at most when they are deleted from the account.
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It is unlikely that AOL keeps backup of emails for long time. But, to confirm that I suggest you to please contact AOL team on this number:***-***-****