If you approch this subject with a politically correct view you can not fire a shot after the last legal minute of hunting light. You must stand back and watch the animal die a slow painfull death.

If you look at it from an ethical view you shoot the deer again and put it down for good even if it is five minutes past legal shooting time.

Any person with a heart does not like to watch a deer suffer.
I personally would shoot the deer again no matter what time of day or night it was.