array (size=2)
0 =>
array (size=1)
'order_id' => '868' (length=3)
1 =>
array (size=1)
'order_id' => '871' (length=3)

$ids = array_reduce($order_id, function($ids, $value){ return array_merge($ids, array_values($value)); }, array());

array (size=2)
0 => '868' (length=3)
1 => '871' (length=3)

如果第二维是数字键名
那么直接这样就可以了：

$result = array_reduce($user, 'array_merge', array())