I am working with a user who has deleted files off of a file share from a domain server, when they re-send a sent message via Outlook 2010 sourcing those now-deleted attachments, they are regenerating on the server in the same location with a datestamp of that moment for Date Modified. 

I have not been able to reproduce this problem using local stores or server shares using Outlook 2013 and the user says it is only he that is affected; the problem began roughly a month ago.  He says that he can replicate it from a different system, however - does anyone know if this behavior is by design for Outlook 2010 or perhaps a bug?  The files are deleted cleanly from the SMB share itself and then show right back up when trying to re-send using that method.

It sounds like he has an attachment management add-in installed. Start troubleshooting with looking at which add-ins this user has enabled.