Draughn played in 20 games for the Kansas City Chiefs and Baltimore Ravens from 2011-13. His best season came in 2012 when he carried the ball 59 times for 233 yards and two touchdowns and caught 24 passes for 158 yards for the Chiefs.
Draughn also returned 23 kickoffs for 537 yards that same year in Kansas City.
Bears general manager Phil Emery served as the Chiefs' director of college scouting when Draughn entered the league in 2011 as an undrafted rookie free agent out of North Carolina. Draughn originally signed with the Washington Redskins before eventually making his way to Kansas City.
The 6-foot, 205 pound tailback appeared in just three games and ran the ball only four times for two yards for the Ravens last season.
The Bears were looking to add depth in the backfield in the offseason after the club released veteran running back Michael Bush on the eve of NFL free agency in March. The team could still decide to draft a running back in the late rounds to compete with the likes of Draughn and Michael Ford for the reserve roster spots behind two-time Pro Bowl starter Matt Forte.