output buffer callback will be called in php request shutdown phase.

and exactly after calling possible destructors of objects.

because there might be some output in object's destructor. 

that means, while in output buffer callback, the global object anotherClass has 
been destroyed.
you can use following codes:

<?php
class AnotherClass{
    public $world = "world";
}
$anotherClass = new AnotherClass();

class TestClass{
    function __construct(){
        global $anotherClass;
        ob_start(function($input) use($anotherClass) {
            return $input.$anotherClass->world;
        });;
    }
}
$tClass = new TestClass();

echo "hello";


which will inc the refcount of $anotherClass , and prevent it be destroyed 
before output buffer callback be called