How to flag node when "event date" has passed and send notice to authors of flagged nodes?
Yes it's perfectly possible to produce such notification using the Rules module. But I don't see any reason why you'd want, or need, to flag (using the Flag module?) such nodes.

Instead you can use an approach which is pretty similar to what I described in my answer to "How to send an email to an author on a specific date using date field specified in a node?", which uses the Rules Scheduler (submodule of Rules):


Change the weaning date to your expiration date.
Add some additional Rules Condition (in Step 3) to avoid sending such notification to checks if the delivery is still outstanding (if it is delivered already, you may not want to send such notification anymore ...). For that you could simply add some boolean field like "Delivered? (Yes/No), which you'd that use in that Rules Condition to be added.


Happy Rules-ing!

PS: should you have some reason to flag the node anyway, then that would be a straight forward enhancement you could add to this solution also.