You're technically supposed to surrender it, but they won't always ask for it, and I haven't heard of a case where they held it against someone who decided to keep it. There's always a chance, though.
If you really want to play it safe, I know of someone who had reported their ARC as lost to immigration and paid for a new card (I think it's only 5k won for a replacement card if reported lost?), then turned in the new card when it was time to leave so that she could keep the old one as a souvenir.