jmike brought this up a couple days ago.
Last pick of the first round, they could just choose not to select anyone and let time expire. They would then have the entire night to work trades, figure out what player they would like to select, etc.
They didnt have this opportunity in 2008 because then the first draft day was 1st and 2nd round combined. (technically they werent picking 32nd that year either, but that didnt make a functional difference)