Over years the Developer may have dozens of sites that s/he does not monitor regularly, and rely on his clients telling him when/if there's an critical error. Typically database and other errors happen silently.

I suggest creating an optional SERVER_ADMIN constant in wp-config.php to help the WP developer be notified of anything critical:

define('SERVER_ADMIN', 'wpdeveloper@example.com');

Then on critical code error points, like:

/wp-includes/functions.php:dead_db()

Add in something like:

// tell server admin of the db failure
if (defined( 'SERVER_ADMIN' ))
  if (!$already_sent_email_today) // some local write cache file
    mail(SERVER_ADMIN, 'Server Database Error', print_r($_SERVER,true).$wpdb->error);

Before the silent HTML error page. Notifying the Server Admin of the critical error.

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An instance where this is handy is if the MySQL database is out of resources. That error occurs silently and sporadically, and will cause a database failure only for a short time, as it's being maxed, the db will run fine again once the requests go down - unbeknown to the server admin (unless monitoring server-side logs).