Ya I was waiting for marius to answer this question. He did it as I expected. I need to mention one more thing along with his answer. You need to call that **"bad controller"** just above your controller definition. That is 

File :`Vendor/AdvancedStock/controllers/ProductController.php`

    <?php    
    require_once(Mage::getModuleDir('controllers','MDN_AdvancedStock').DS.'ProductController.php');
    class Vendor_AdvancedStock_ProductController extends MDN_AdvancedStock_ProductController
    {
         // some code
    }

I told so because, as per my knowledge magento will not include the class that you are going to rewrite, if that class stands for a controller.  For block rewrite, helper rewrite you may not require this step. Since magento will do that job for us.