Draughn appeared in five games this season. Turbin made his Cleveland debut in Sunday's overtime loss to Denver, gaining 27 yards on 10 carries. Draughn also handled kickoff return duties earlier this season before he was replaced by Justin Gilbert.
The Browns also signed linebacker Jayson DiManche off Kansas City's practice squad. The 6-foot-1, 245-pounder has appeared in 28 NFL games. He was waived by Cincinnati on Sept. 11.
Leonhardt was originally signed by Oakland as an undrafted free agent in 2013. He appeared in 12 games and made three starts last season with the Raiders.
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