The NFL Draft designates the last player drafted as such.
According to NFL.com's historical draft database, the first Rutgers player drafted was Linebacker Bob Simms who was drafted in the 10th round in the 1960 NFL Draft by the New York Giants.
Jimmy Walker of Providence College. He was selected 1st overall in the 1967 NBA draft by the Detroit Pistons and last overall (445th) in the 1967 NFL draft by the New Orleans Saints.
Pat McAfee, drafted in the 7th round of the 2009 NFL Draft by the Indianapolis Colts.
Yes. When a player is drafted during the NFL draft the team that drafted them owns the signing rights. So, if the player refuses to play they will have to wait a year and then get signed as a free agent. If that team doesn't do anything with the signing rights to the player they will not play in the NFL that year. If a player is not drafted they become an 'undrafted free agent' and are immediately available to be picked up by any team.
David Terrell
"Mr. Irrelevant", the last pick in the 1996 draft, was New Mexico State LB Sam Manuel. He was drafted by the 49ers. He never went anywhere in the NFL.
David Johnson was taken by the Pittsburgh Steelers last overall in the 2009 NFL draft.
Cobb was drafted in the 2nd round (64th overall) of the 2011 NFL Draft by the Green Bay Packers.
a big fat 0
Redskins
Nope, they are going to be admitted to a free agent