Execute Closing Shortcode After the_content

Maybe I misunderstand what you are doing, and I apologize if that is the case, but…

1. It looks like you are returning content if the post DOES NOT already
   have one, which looks backward to me based on my understanding of
   your problem.
2. It looks like you are trying to execute a broken
   (incomplete) shortcode.

I misunderstood the original question but based on comments below, you need to run do_shortcode() on the whole content block, not just on the closing section.

I think your code should look like:

add_filter( 'the_content', 'closing_shortcode' );
function closing_shortcode( $content ) {

        // return if the shortcode has already been added
        // Note the ! was removed
        if( has_shortcode( $content, 'members') )
        return $content;

        // Add the closing sortcode tag
        $close_shortcode="[/member]";

       // and run do_shortcode() on the whole content block
        return do_shortcode($content . $close_shortcode);
}      

If that doesn’t work, it will take some manipulation of the core content and shortcode execution systems and I will have to tackle later, when I have more time.