Should Woodard clear waivers tomorrow, he would revert to the Dolphins’ injured serve list.
Smith, 26, wound up going undrafted out of Florida State back in 2016. He later signed on with the Chiefs and was on and off of their roster during his rookie season.
Smith returned to the Chiefs last year on an exclusive rights contract. However, Kansas City declined to tender him a restricted offer this offseason.
Smith is working his way back from a torn ACL he suffered last October.
For his career, Smith has appeared in 31 games over the course of three seasons for the Chiefs and recorded 29 tackles, one sack, an interception and two pass defenses.