It may end up being irrelevant when the NFL schedules the 2013 Supplemental Draft, because as of this writing there aren't any entrants. But in the event we do get any entrants, the draft will take place on July 11, 2013.
The Supplemental Draft's drawn more than the usual amount of attention in the past two years thanks to a pair of high-profile players -- Terrelle Pryor and Josh Gordon -- being selected in early rounds.
Pryor was a third-round supplemental selection for the Raiders in 2011 (meaning they sacrificed a third-round pick in the 2012 NFL Draft) and Gordon was a second-round supplemental selection by the Browns in 2012 (the Browns forfeited their second-round selection in the 2013 NFL Draft as a result).
Though Pryor hasn't, um, worked out yet, he does offer some upside. (Maybe, right? Right??) And Gordon projects as a potential breakout player in 2013 -- he produced a very nice statline in 2012 despite not having played football for a year.
Sims contemplated leaving Houston for the 2013 NFL Draft but ultimately opted to return and then in late May, decided to leave the team. Whether or not he'll be eligible for the Supplemental Draft remains to be seen and he could end up deciding whether the NFL holds one this year or not.