How to delete orphan userdata from array in wp-options

If what posted is all the code you are using, you unsetting the value from the retreved array using unset, but then you don’t save again the array on database:

add_action( 'delete_user', 'forum_remove_deleted_user' );

function forum_remove_deleted_user($user_id) {   
    $user_obj = get_userdata($user_id); 

    $subscbr_email = $user_obj->user_email;

    if( ! empty( $subscbr_email ) ) {                    
        $list = (array) get_option('mf_forum_subscribers_1');

        if( ! empty($list) && ( false !== array_search($subscbr_email, $list) ) ) {

            $key = array_search( $subscbr_email, $list );
            unset( $list[$key] );

            update_option('mf_forum_subscribers_1', $list); // you miss this part
        }               
    }       
}

For sake of semplicity I removed the dependency from is_subscribed function that is unneeded here.