Winn was in jeopardy of being cut last week, a casualty of Cleveland's improved depth on its defensive front. He made the 53-man roster only to be dealt two days before the season opener against the New York Jets.
The 6-foot-4, 300-pounder was selected in the sixth round of the 2012 draft out of Boise State. He appeared in 40 games, making 18 starts. He recorded 87 tackles, three sacks and made two interceptions.
Last season, Winn had a career-high 31 tackles and made a leaping block of a field goal in a win over Tampa Bay.
The Browns are expected to fill his roster spot by promoting running back Shaun Draughn from the practice squad.
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