Allow a subscriber to be an author and view only his post

You must write a small plugin for the Hook pre_get_posts; an example:

add_action( 'pre_get_posts', 'fb_allow_draft' );

function fb_allow_draft( $query_obj ) {
    // only on admin screen use this filter
    if( ! is_admin() )
        return;

    // change our query object to include any post status
    $query_obj->query_vars['post_status'] = 'any';
}

If you will specific this new loop for an rights object from an role, use the small question: if ( ! current_user_can( 'read' ) ) return;