Bass, an undrafted free agent out of Texas A&M in 2012, has bounced back and forth from the Cowboys roster over the past two seasons.
The 6-foot-5, 294-pounder has appeared in two NFL games, both during the 2012 season. He did not play in a game during the 2013 season as injuries forced him to the injured reserve list.
Bass adds depth along the defensive line, as the Patriots have been without defensive tackles Sealver Siliga (left hand) and Chris Jones (left ankle) in recent practices due to injury. Bass himself is currently working through a hamstring injury.
Health has been a key focus along the Patriots defensive line throughout the offseason, as veterans Vince Wilfork (Achilles) and Tommy Kelly (ACL) are coming back from major injuries, while first-round pick Dominique Easley is still working to get back to 100 percent after an ACL tear during his final college season.
Green, an undrafted free agent out of Illinois last offseason, bounced back and forth from the Patriots' active roster and practice squad. He appeared in two games, but did not record a statistic.
The Cowboys are searching for cornerback depth as they continue to deal with an injury to Morris Claiborne, while the NFL announced a four-game suspension for veteran Orlando Scandrick on Monday. Brandon Carr recently returned to the team after spending time with his family following the death of his mother.
Cornerback has become an area of depth for the Patriots this offseason after adding veterans Darrelle Revis and Brandon Browner to a core that also includes Alfonzo Dennard, Logan Ryan and Kyle Arrington.