From what I know pretty much everywhere except Le Mans 24h a car will be classified even if it doesn't finish as long ir completes a certain % of the distance covered by the leader (in most cases 70%).
Quote:
Originally Posted by Tim the Grey
Any race ends after the lead car crosses the line the first time after elapsed time is up. Any car crossing the line after that, has ended their race.
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This may vary from series to series, at least it did in the past. I've definitely heard of races where the first car to cross the line after the time runs out is the one that is shown the checkered flag first.