When a cPanel account has the default/catch-all email address set as the cPanel username and Exim reports
email@example.com is undeliverable: The mail server could not deliver mail to firstname.lastname@example.org . The account or domain may not exist, they may be blacklisted, or missing the proper dns entries.
and the account never receives the email.
This issue occurs because Exim doesn't have a configuration set for the hostname and should exist in /etc/localdomains
If this hostname doesn't exist in /etc/localdomains it can easily be added with
echo $(hostname) >> /etc/localdomains