This the most voted-for quiz feature request, and we very nearly have a solution. It is the problem of what to do if time expires when the student is offline.
I think have finished the code, and I am hoping to submit it for integration at the end of the week, so there is not much time, but if anyone can do a bit of testing, that would be very helpful. (We will be doing some more testing at the OU.)
After these changes have been integrated, we will then move into the Moodle 2.3 beta-testing period, and that is a chance for you to do more testing before Moodle 2.3 is released at the start of June.
The only documentation at the moment is the design documentation I wrote before making the change: http://docs.moodle.org/dev/Better_handling_of_overdue_quiz_attempts
If you want to test, you really need to get the code from git. Follow the link in MDL-3030, which I suppose might lead you to the Zip button on https://github.com/timhunt/moodle/tree/MDL-3030 to download a zip file.