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.