Kase, 24, drew interest leading up to the trade deadline as a cheaper option for those who couldn't land a big name like Chris Kreider. A productive two-way winger when healthy, Kase has another year left on his contract at a manageable $2.6 million, but health has been an issue.
Kase scored 20 goals in his second season in 2017-18, but a variety of injuries limited him to 30 games last season, when he scored 11 goals and had 20 points. He has rebounded this season with seven goals and 16 assists in 49 games.
The Ducks are in rebuilding mode, sitting seventh in the Pacific Division after missing the playoffs last season for the first time in six years.
Backes, a 14-year NHL veteran, was assigned to AHL Providence in January after clearing waivers. He has 245 goals with 309 assists in 944 NHL games, spending the first 10 years of his career with the St. Louis Blues and the past four in Boston. A two-time U.S. Olympian, he was an All-Star in 2011 and was the runner-up in Selke Award voting the next season.
Backes, 35, had just one goal and two assists in 16 games with the Bruins this season. He was injured in a scary collision with the Senators' Scott Sabourin in November and missed almost a month.
The Bruins will retain 25% of Backes' salary.
Andersson, a 20-year-old defenseman, was playing for Moncton of the Quebec Major Junior Hockey League this season and had two goals and 20 assists.
The Associated Press contributed to this report.