The Events Calendar
The Events Calendar does not store media, but it ships a placeholder file that it expects to find under a fixed name. The compatibility skips cache busting for those internal template assets so the plugin keeps working with cache busting enabled.
WP-Stateless 4.4.3 still includes this as a built-in compatibility (enable it on the Compatibility tab or with WP_STATELESS_COMPATIBILITY_THEEVENTSCALENDAR). A standalone addon, WP-Stateless for The Events Calendar, is published on wordpress.org as well.
Tested with The Events Calendar 6.15.16.