RSS feed for the previous week’s posts

You could try to modify the feed query directly via:

/**
 * Modify the main feed query to show posts from the previous week, 
 * when the GET parameter wpse_previous_week is set
 *
 * @link http://wordpress.stackexchange.com/a/194843/26350
 */
add_action( 'pre_get_posts', function( $q )
{
    if(    $q->is_feed() 
        && filter_input( INPUT_GET, 'wpse_previous_week', FILTER_SANITIZE_NUMBER_INT ) 
    )
        $q->set( 'date_query', 
            [
                [ 
                    'before'    => 'Sunday previous week', 
                    'after'     => 'Monday previous week',
                    'inclusive' => true 
                ]
            ] 
        );
} ); 

and view the feed with:

example.tld/feed/?wpse_previous_week=1

Note that you might have to test and modify the date strings to better suit your needs.