This can generate the string "Mailbox is empty" right after a call to imap_open().  That's not an error.  That means something like this is not good enough to know the open failed due to a wrong password or host name or whatever. This

  $imap = @imap_open( $mailbox, $user, $pass); 
  $errors = @imap_errors();
  if ( $errors ) {
      echo 'Login failed: ' . implode ('; ', $errors );
  }

can output "Login failed: Mailbox is empty" which is silly.

Instead, check the return value from imap_open().

  $imap = @imap_open( $mailbox, $user, $pass); 
  if ( ! $imap ) {
      $errors = @imap_errors();
      echo 'Login failed: ' . implode ('; ', $errors );
  }