The 2015 NFL Supplemental Draft is scheduled for July 9 this year.
The Supplemental Draft includes players who were for various reasons not in the real draft. This year there are several prospects who are entering the Supplemental Draft but just one that will garner some attention: Clemson OT Isaiah Battle.
The way the Supplemental Draft works is if the Chiefs wanted to submit a bid on Battle, they would do so. The bid would be the round that the Chiefs would select that player. If they're the highest bid, they win the rights to the player BUT they lose the corresponding pick for the (real) 2016 draft.
The idea of using a late round pick on a promising offensive tackle should be intriguing to the Chiefs. They need to continue stock piling talent, especially at tackle where Donald Stephenson will become a free agent at the end of the season. The Chiefs have a number of offensive line options that they would need to work out before considering Battle.
The last time a Supplemental Draft pick was used was in 2012 when the Cleveland Browns won his rights with a second round pick.
Per PFT, other players in the Supplemental Draft include West Georgia DT Dalvon Stuckey, West Georgia DE Darrius Caldwell and North Carolina Central WR / KR Adrian Wilkins.