He played in five games this season, appearing on special teams, but was not credited with a tackle.
Moore spent his rookie season on IR and then started four of 13 games he played last season before a knee injury put him on IR again.
It's pretty obvious by now the previous regime made a bad mistake by taking Moore 49th overall in 2003, particularly when wide receiver Anquan Boldin was available, and it's a legitimate question to ask whether Moore ever will make any kind of impact in Miami.
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As for Shawn, he was in camp with the Dolphins this year before being released on Sept. 4. He was re-signed on Oct. 12 but released three days later.
Shaw, who played for Nick Saban at Michigan State in 1998 and 1999, appeared in four games for the Dolphins last season.
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The Dolphins also made a move on their practice squad, signing wide receiver Jason Willis and releasing kicker Jeff Chandler. Chandler had been signed last week as insurance because of Olindo Mare's knee injury, but Mare answered the call against New Orleans last Sunday and made 4 of 5 field goal attempts.
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One player who did not practice was wide receiver David Boston. Saban said it was just a matter of dealing with a knee problem that's been bothering Boston on and off all season.