I was working on a Windows domain workstation. I opened an email with a Word document attached. I made edits and saved the document. To what directory was the document saved?
The file is saved on the local machine. As long as you are still logged into the machine, you should be able to access it. (Not sure whether the file persists, or for how long) after the user logs out of the Windows domain session.
For Mozilla Firefox, you can find the document by following the menu path: Tools > Downloads. If you open the file from there, the changes should be there. You can also right click on the icon for the document, and select Open containing folder to see the location of the file.
Internet Explorer will likely have different behavior. We do have a Win.mit.edu machine in the Call Center for test purposes.