When a member sends a private message to another member but has their account deleted via ACP (before the recipient reads the private message), the recipient has a constant notification of that message but nothing listed in their inbox.

The issue is caused by the entry in phpbb_users > user_new_privmsg column. When the user was deleted, the entry isn't reduced by 1.

To recreate: Create a new user account and from the new user account send a private message to an admin. Now login with the admin account that the private message was sent to but don't read the private message or clear the notification, go straight to ACP and delete the new user account that sent you the private message. Navigate back to board index and the notification of a new private message is still delayed and you cannot clear it! Your inbox will be empty.

https://www.phpbb.com/community/viewtopic.php?f=556&t=2519011