Fatal error after editing or deleting custom Panels layout as of CTools 7.x-1.6-rc1

When I delete a custom Panels layout or edit a custom layout directory and .inc file name, I get the following error with CTools 7.x-1.6-rc1 or later installed.

Fatal error: require_once(): Failed opening required '[path-to-theme-custom-layouts-directory]/two-column-layout/two-column-layout.inc' (include_path='.:/usr/lib/php') in sites/all/modules/ctools/includes/plugins.inc on line 470

Deleting an entire theme will also produce this error (even when the theme is disabled) if it contains custom layouts.

This issue also reported here #2461809: Cannot delete custom theme layout directory.