Well, you do not say what you expect it to do, but I suspect what you are trying would require the use of [man]eval/man, e.g.:
$theArrayEntry = " 16=>array('?dt=xx','linked-day'),
21=>array('?dt=xx','linked-day') ";
eval('$days = array(' . $theArrayEntry . ');');
As to why you would want to do it, I have no idea. 😉