If you don't want the student to retake the entire quiz:

1. Go to the quiz and select edit settings.
2. Under timing: Set the close date so that it is after the current day.
3. Set When times expires to There is a grace period...
4. 
   
5. Under grade: set Attempts allowed to Unlimited.
6. 
7. Under question behavior: Set Each attempt builds on last to Yes.
8. 
9. Invite students who did not submit quiz to do so.
10. Allow them to start a new attempt, and close it immediately after.

If the student didn't finish on time, and you still want to grade the non-submitted quiz:

1. Go to the quiz. Click the gear and then Edit settings.
2. Under timing: Make sure When time expires is set to Open attempts are submitted automatically.
3. 
4. Quiz will go into gradebook after time expires regardless if it was submitted or not.