Usually, the undelivered message can contain something useful. If the server is full; it has reached it's maximum quota then it cannot receive any more new mail. In these cases the sender will get a message that the email could not be delivered. You will not receive new mail on server and therefore will not get any new mail in Thunderbird. If you are using POP mail account then perhaps you have tons of emails on server. Maybe the server Spam folder has emails as well. Suggest you logon to your webmail account. Empty the 'Spam folder. Delete a load of old messages to free up space. Do you regularly compact the Inbox, Junk and Drafts folders to remove all traces of hidden marked as delted emails? If you have an IMAP mail account, check to see what it says for your quota. right click on imap mail account 'Inbox' folder and select 'Properties', then select the 'Quota' tab. If this is a gmail account then you may have deleted emails not realising you have only been deleting labels and not the emails themselves in which case the 'All Mail' folder will be huge with archived mail you thought were deleted. If you need to keep emails but free space on server. Synchronise imap folders for offline use and in Offline mode, copy emails to 'Local Folders ' mail account. If you can read them in Offline mode in Local folders then you have a good copy. Make a backup of the profile 'Thunderbird' folder. Then remove emails off server to free space. then compact the 'Inbox' or select to use the Account Settings option to expunge Inbox on Exit. This will auto compact the Inbox. Suggest you logon to webmail account and make sure you have freed up space for new incoming mail.