If signed, Barwin could become one of the Rams' starting outside linebackers, while Dunbar could replace free agent Benny Cunningham as a third-down back.
Barwin played under new Rams defensive coordinator Wade Phillips while with the Texans from 2011 to '12. The 30-year-old has spent the last four years with the Eagles, but last year converted from an outside linebacker to a defensive end when the team began to run a 4-3.
Barwin has started 96 consecutive games dating back to 2011, compiling 46 sacks, 225 solo tackles, six forced fumbles and 36 pass deflections during that span. But he struggled with his position change in 2016, ultimately graded 100th among 109 qualified edge defenders by Pro Football Focus, and the Eagles released him last week, saving $7.75 million in salary-cap space. Joining the Rams may give him a chance to return to a scheme he is more accustomed to.
Dunbar, undrafted out of North Texas, has been buried in the Cowboys' depth chart for most of his career but offers versatility.
The 27-year-old is a solid pass-catcher out of the backfield and also has some experience returning kickoffs, a role Cunningham filled with the Rams. In 54 games from 2012 to '16, Dunbar rushed for 422 yards on 94 attempts and also made 68 catches for 646 yards. The Rams currently have only Aaron Green and Malcolm Brown, two undrafted free agents, behind their featured running back, Todd Gurley. At linebacker, they have Mark Barron, Alec Ogletree and Robert Quinn, who will be converting from defensive end as the Rams transition to a 3-4.
ESPN's Adam Caplan first reported Dunbar's visit, while Barwin's visit was first reported by the Los Angeles Times.