Access child property from parent scope

I need a parent class to access its child properties:

class Parent {
  private $_fields = null;

  public function do_something() {
    // Access $_fields and $child_var here
  }
}

class Child extends Parent {
  private $child_var = 'hello';
}

$child = new Child();
$child->do_something();

When $_fields is modified from the child scope, it's still null in the parent scope. When trying to access $child_var from parent scope using $this->child_var, it's of course undefined.

I didn't find anything like a "function set" that would just be copied in the child class...