Currently, the only way to override the HTTP 500 error message "Fatal error: The web server did not finish its request" is to customize kernel/private/classes/ezpkernelweb.php. Please create a mechanism (through an additional setting, for example) to allow for that in a clean, user-friendly way.

Note: using Apache custom error responses via ErrorDocument 500 would seem a good alternative, but it doesn't work:

https://issues.apache.org/bugzilla/show_bug.cgi?id=34094
http://stackoverflow.com/questions/2252624/apache-errordocument-not-working-for-php-500-error
http://stackoverflow.com/questions/5765319/apaches-errordocument-directive-does-not-redirect/5839076#5839076

The actual ErrorDocument documentation (http://httpd.apache.org/docs/current/mod/core.html#errordocument) states:

Although most error messages can be overridden, there are certain circumstances where the internal messages are used regardless of the setting of ErrorDocument. In particular, if a malformed request is detected, normal request processing will be immediately halted and the internal error message returned. This is necessary to guard against security problems caused by bad requests.