Custom Rewrite rule to match anything not already matched by WordPress

You can’t do that with a rewrite rule, the regular page rule already matches, but you can intercept the data that’s extracted from that rule before it gets transformed into a query.

We do that by hooking the parse_request action, where we can check for a custom slug, and modify the request object directly. I recommend you var_dump($query) and have a look at the whole object for different kinds of requests. See comments in code.

add_action( 'parse_request', 'wpd_check_for_my_custom_slug' );
function wpd_check_for_my_custom_slug( $query ) {
    if( isset( $query->query_vars['pagename'] ) ){
        // check if the slug matches some custom content
        // replace this with your query code
        if( 'my-custom-slug' == $query->query_vars['pagename'] ){
            // the request is for a custom slug
            // store the originally requested slug
            $query->query_vars['my_special_var'] = $query->query_vars['pagename'];
            // and load a placeholder page
            $query->query_vars['pagename'] = 'placeholder-page';
        }
    }
}

Note that if your permalink structure is just %postname%, the slug will be in name, not pagename. You will then also have to unset name after.

If you plan to load a theme file at the end of this process, I suggest using a placeholder page of the page post type for these requests. WordPress expects some kind of post object to exist for a template to successfully render. You can filter and override all of the titles, content, etc..

If you plan on outputting something completely custom, you could load that and just exit here.