Steps to recreate:
1) Setup a template file and corresponding hook_theme() entry.
2) View a page that uses that template. It works!
3) Edit your code to rename the template file (both the file name and the hook_theme entry)
4) Reload the page.
5) See this useless error message:
Twig_Error_Loader: Unable to find template "modules/drupalgotchi/templates/drupalgotchi-status-block.html.twig" (looked into: /stor/sandboxes/garfield/wscci/www/wscci) in "core/modules/block/templates/block.html.twig" at line 52. in Twig_Loader_Filesystem->findTemplate() (line 197 of /stor/sandboxes/garfield/wscci/www/wscci/core/vendor/twig/twig/lib/Twig/Loader/Filesystem.php).
Catch that exception (I assume it's an exception...), log it, and have the theme call simply return an empty string. We did that back in Drupal 7 (after we fixed the silent, undetectable fail of Drupal 6), and we should keep doing it.