You have to re-implment base class method; try with:
class Derived extends Base {
protected static $c = 'derived';
public static function getC() {
return self::$c;
}
}
As you see, this solution is very useless, because force to re-write all subclassed methods.
The value of self::$c depends only on the class where the method was actually implemented, not the class from which it was called.