rest - attribute added to MessageContext in request don't show up in exception chain

Question

I have a custom RequestHandler where I do some logic, and then add an attribute to the MessageContext so that I can retrieve it in all my Resources (via the @Context annotation). This works great. On the response, I need to access this same attribute. I am able to retrieve it if my Resource method returns successfully, but not if an exception is thrown. Is it possible to get this same attributes on the MessageContext somehow, even when an exception is thrown? I use a custom ExceptionMapper, so I need to throw an exception if it doesn't complete properly.