In case exim can not deliver a mail, it informs the sender by sending a warning message. To send out those messages only after a mail could not be delivered for 15 days, add the line

delay_warning = 15d

somewhere close to

timeout_frozen_after = ... 

in exims configuration file. The latter does - at least on debian systems - already exist. On Debian systems, there is no exim4.conf file. You have to edit exim4.conf.template instead and run update-exim2.conf afterwards.

exim4 -Mg <Message-Id>

Place virtual hosts alias files (like /etc/aliases) in /etc/exim4/virtual/ with it's name being the domain name. I.e. for domain example.com it would be the file /etc/exim4/virtual/example.com.

Create the file /etc/exim4/conf.d/router/350_local_virtual:

virtual:
      driver = redirect
      allow_defer
      allow_fail
      domains = dsearch;/etc/exim4/virtual
      data = ${expand:${lookup{$local_part}lsearch*@{/etc/exim4/virtual/$domain}}}
      retry_use_local_part
      pipe_transport   = address_pipe
      file_transport   = address_file
      no_more

Then run

update-exim4.conf.templage -r
/etc/init.d/exim4 restart

You must not have a virtual domain name for the “system mail name” as configured with dpkg-reconfigure exim4-config as this will screw up delivery to local addresses.