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Subscriptions sent from Tableau Server/Online send a screenshot of the dashboard and a link to access it.
Sending the .twbx file directly is not currently available, but you can vote for this Idea on the Ideas forum: Ideas
You could also achieve this by coding a script using Tableau's APIs: Tableau's Developer Tools & APIs
Unfortunately there is no way to do this natively. However, you can use the tabcmd get command to retrieve a packaged workbook from the server. You may use this combined with a third-party script to automate pulling down the .twbx and sending it via email.
Reference: tabcmd Commands - get url