You can check in the 'Trash' folder, for the deleted mails !
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Did you enable the "Leave message on the server" option for outlook or similar option for Thunderbird? If you didn't enable this option, means that all emails are downloaded to the mail client. If you deleted the mails from your mail client, they are going to the "deleted items", and if you have permanently delete the mails from the "deleted items", your emails are lost forever.
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