The supplemental draft accounts for players who did not declare for the traditional spring draft but are eligible to enter the NFL; they are at least three years removed from high school. Usually their college circumstances have changed in some way since the January declaration window, be it NCAA discipline or academic troubles, or both. Such players can petition for supplemental draft eligibility.
Teams are separated into three groups based on the previous season; the first group are non-playoff teams that had six or fewer wins.
The second group are non-playoff teams with more six wins.
And the final group are playoff teams.
The order in those groups are determined by a weighted lottery with the teams with the fewest wins given the best chance to win the earliest picks. Bids for players are submitted blindly by teams with the round that given team would want to select a given player.
After the order is determined, each team submits to the league the name of the player(s) they are interested in, as well as the round of the supplemental draft they would like to choose them in. The team that submits the highest bid is awarded rights to the player. If more than one team bids a pick from the same round, the team with the highest pick in the round wins.
A total of 44 players have been selected in the supplemental draft since 1977, including Patriots WR Josh Gordon and 2018 pick Sam Beal of the NY Giants.
If you would like to see if you are eligible for the Supplemental Draft you need to call the NFL Offices in New York, to begin the petition.