4. Trent Brown
Trent Brown made headlines in 2023 for all of the wrong reasons. The offensive tackle struggled with injuries all season, and was inactive for six games scattered throughout the schedule. He was a healthy scratch for the team's Week 17 loss at Buffalo and was also inactive for the Week 18 finale at home against the New York Jets. However, most of the trouble with Brown came off of the gridiron.
In November, Albert Breer of Sports Illustrated's Monday Morning Quarterback reported that the tackle was "habitually late to things" after Brown was left behind stateside for the team's overseas trip to Germany. A Boston Herald report also claimed that Brown "openly discussed plans to play for an NFC team" in the Patriots locker room a day after the team's Thursday Night Football win over the Pittsburgh Steelers.
More directly, Brown denied that he had discussed playing for another team and explained that a litany of illnesses had prevented him from playing several games.
Brown will be 31 at the start of the 2024 season, and is ranked as the 22nd-best free agent overall by Pro Football Focus. Perhaps Brown's contentious relationship with the Patriots has been ameliorated by the departure of Belichick and the hiring of new head coach Jerod Mayo, but there just appears to be too much past conflict for a re-signing to make sense for both parties.