How can I change the term “Published” next to # of posts published on WordPress dashboard All Posts page?

In your theme’s functions.php or in a plugin:

function prattle_custom_text( $input ) {
    if( is_admin() && 'Published' == $input ) {
        return 'Saved';
    }
    return $input;
}
add_filter( 'gettext', 'prattle_custom_text' );

It’s a tid bit dirty, but it’ll do the job.