It it is a checkbox field then you need to update it with an array of the values you want checked, each value is not stored separately.
$status_active = get_field('status_active', $post_id);
if (!in_array('status_locked', $status_active)) {
$status_active[] = 'status_locked';
update_field('status_active', $status_active, $post_id);
};