Participants Database avoids loading it's content and assets on pages that don't have Participants Database content. Since the plugin is shortcode-based, it does this by inspecting the content of the current page and fires an action (pdb-shortcode_present) if a Participants Database shortcode is on the page.
With some types if shortcode placement (such as in a widget), the shortcode isn't actually in the page content, so the plugin doesn't know to load the assets. This code snippet provides a way to let Participants Database know it should load its assets on a particular page.
In the example, the page has an ID of 9727. Change that to be the post ID of the page you need the trigger the asset load on.