The Red Sox envisioned Thornburg as a key piece, a set-up man for closer Craig Kimbrel, and were willing to part with Shaw, who had shown power as a versatile infielder for the Red Sox in 2016.
Thornburg missed the entire 2017 season after being sidelined for thoracic outlet syndrome surgery. He pitched in only 41 games over the next two seasons because of injuries and ineffectiveness. His career with the Red Sox ended with 42 2/3 innings pitched, a 2-0 record and a 6.54 ERA.
Shaw, meanwhile, became the Brewers' everyday third baseman, slugging 31 homers in 2017 and 32 in 2018. He has struggled this season, hitting .164 with six homers in 57 games before being sent down to Triple-A on June 28.
Dubon, a middle infielder, made his first major league appearance on Sunday. Dubon was hitting .307 with 14 home runs and 42 runs batted in over 83 games for Triple-A San Antonio this season.