How to show 404 page for not found images If I request an image that doesn't exist like mysite.com/test/test_not_found_image.jpg, I get a Not Found white page just like this page: https://www.drupal.org/files/testing_404.jpg.

Is it possible to have Drupal show the styled 404 page that I have instead of that white 404 page?
While @Shawn Conn's answer does work it does cause issues in Drupal because of image cache. If you go to a page that doesn't have the image style created yet it won't create the image because of the .htaccess rule.

The best way to display a 404 page on bad images is to use the Fast 404 module and create a static html page.