I haven't used the IMAP4Get component so I'm not sure exactly how it works. If you have checked the Delete After Retrieve checkbox you could simply have the Exception process I described return to the IMAP4 Get component after verifying the ExceptionComponentName and ExceptionTriggerMessage.
If you are not using the Delete After Retrieve option, you can try to re-engineer your process somewhat.
I found a discussion at https://www-secure.symantec.com/connect/forums/email-inbox-monitor which included the following:
2. Use the "IMAP4 List" component (or POP3 List) to gather unread messages from your Exchange inbox. This will give you an array of the messages in the inbox. You will have to be able to connect via IMAP or POP for this to work.
3. Use the "For Each Element In List" component to setup a loop to go through the array of email messages. This will give you the "EmailHeaderType", which includes the Email ID.
4. Use the "IMAP4 Get By Id" component to get the contents of each message in the list. You use the Email ID from the For loop to get the contents of the message. Then you can do whatever you want with the contents.
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If the IMAP4 List component is able to process the messages that lack a From Address you would have access to the Email ID of each message as it is being processed (in the loop). If a message generates an exception, you could use the IMAP4 Delete By Id component to remove it (after verifying the ExceptionComponentName and ExceptionTriggerMessage)