Hi James,
This can be easily achieved with a custom field built on superclass level - Cases entity. Once you re-create Closed in Build field on a cases entity, you will be able to access/update this field from all its subclasses: bugs, issues, requests and risks.
If you would like further assistance building such custom field, hop our our free Advanced Office Hours Webinars ( http://www.clarizen.com/live-demo.html#second and we will be happy to walk you through this.
All the best,
Diana