Vigil (back) was placed on the Dolphins' reserve/NFI list on Tuesday.
Vigil has been dealing with a nagging back injury as of late, and will now be sidelined for the first six weeks of the regular season. When healthy, he'll likely return to a special teams role in which he recorded 18 tackles and a blocked punt across 16 games during the 2015 campaign.
Jordan (knee) will be placed on the reserve/non-football injury list to start the season, ruling him out for the first six weeks, NFL.com's Ian Rapoport reports.
Picked No. 3 overall in 2013, the 26-year-old Jordan was suspended for all of 2015 due to a repeat violation of the NFL's substance abuse policy. Although he was conditionally reinstated by the league, Jordan hasn't been able to practice while recovering from offseason knee surgery. He has just three sacks in 16 career appearances.
Petty (shoulder) has been ruled out of Sunday's game against the Chiefs.
Petty's shoulder injury continued to keep him sidelined through practice this week and will leave him inactive for a third straight game to begin his career. As a result, Geno Smith will serve as the Jets' backup to starting quarterback Ryan Fitzpatrick this Sunday.
McDougle was waived by the Jets on Sunday, Adam Schefter of ESPN reports.
McDougle was originally drafted in the third round of the 2014 draft, but his rookie season was quickly derailed by a torn ACL. The Jets had hoped that McDougle would rebound in 2015, but the 25-year-old never seemed to return to his old self after the injury.
Williams (concussion) will not play in Saturday's preseason game against the Giants.
Even if he were healthy, Williams would face long odds to make the final roster. Matt Forte, Bilal Powell and Khiry Robinson are all locks, and Antone Smith was recently signed to compete for the No. 4 job.