Given that you really don’t have a fake student in Moodle, it’s difficult for teachers to see how students view the results of their quizzes.
Here’s what you should tell students to do:
1. Select the link for the Moodle quiz or exam in the course.
2. Select picture link (will open in new window) and to see any one of the three links that a student could choose to view results of her individual quiz/exam.
If you are seeing students’ quiz results with a grade of zero and a time spent over the quiz which is greater than the quiz duration you’ve set, here’s why:
A student is given a zero if (1) he disables javascript in his browser which prevents Moodle from automatically submitting his quiz at the end of the duration AND (2) he has gone over the quiz duration you’ve set by MORE than 60 seconds. No javascript means NO counter as well

Students are given a warning that JavaScript must be enabled to continute with the quiz, but the system does not stop them from taking a quiz.
They can still take the quiz but they can get into trouble IF they go over your duration by MORE than 60 seconds. You as the teacher will also see that he went over the duration in my example below by more than 60 seconds which gave him a zero even though he got one correct. My quiz was set for 1 minute but with no javascript enabled the student could take longer before saving and submitting his quiz.

This example shows what a teacher will see if a quiz is taken without javascript enabled. The student exceeded the quiz time limit and the grade is 0.
How do you enable javascript in your Internet browser?
Look for the preferences option in your browser menus and select/enable the javascript option. Then restart or close and reopen your browser.
Finally, if a student closes his Internet browser window before the quiz duration has ended, the Moodle system will warn him that ANY questions he may have answered to that point will not be saved (see example below).

Changes will be lost message.
Also, the Moodle quiz system will continue to count down as though the student were still taking the quiz. And if for some reason, the student does not reattempt the quiz before the duration has ended, the student will get a zero for his quiz score.

Quiz score showing 0.