Demps played for the Kansas City Chiefs last season and has previous stops in Philadelphia (two seasons) and Houston (three).
Last season, he was third in the NFL with a 30.1-yard kickoff return average on 33 runbacks, including a 95-yard touchdown at Washington on Dec. 8. He also led the Chiefs with four interceptions.
Demps entered the NFL as a fourth-round draft choice of the Eagles in 2008.
Thurmond spent his first four NFL seasons with Seattle, which selected him in the fourth round of the 2010 draft.
Thurmond played in 34 regular-season games with eight starts and made his only start in five postseason games in the Super Bowl. He was limited to six games in 2011 and two in 2012 because of injuries.
Last season, Thurmond played in 12 regular-season games with three starts. He missed four games while serving a suspension for violating the NFL's substance-abuse policy. Thurmond returned for the regular-season finale against St. Louis and played in all three postseason games.