As expected, the Detroit Lions did not select anybody in the 2012 NFL Supplemental Draft. Actually, only one player was selected during the entire draft -- Baylor wide receiver Josh Gordon. The Cleveland Browns submitted a second-round pick (!) for Gordon, meaning they will forfeit their second-rounder in the 2013 NFL Draft.
The one interesting thing about this year's supplemental draft as it relates to the Lions is that they had the second-to-last pick in each round, according to Jason La Canfora. The supplemental draft order is determined by a weighted lottery, and the Lions were apparently pretty unlucky to end up at the bottom of each round. It didn't matter since the Lions didn't select anybody, but it's worth noting nonetheless. (For more on how the order is determined, check out Pro Football Talk's article on it.)
With the Lions again not selecting any players in the supplemental draft, their streak of sitting it out continues. The Lions haven't used a pick in the supplemental draft since 1982, when they picked defensive backwith a ninth-round selection. In every year since then, they have passed on giving up a future pick for a player in the supplemental draft.