Andrei Markov has begun to struggle a bit on the defensive side of the game, and although I think Alexei Emelin has a lot of good qualities, he hasn't been helping Markov out in this area. With Raphael Diaz skating now, but still uncertain to return any time soon, the Canadiens could really be put over the top by upgrading their top 4 D.
One player who may be available for a reasonable price is Dallas Stars veteran Stephane Robidas. Robidas is on an incredibly reasonable cap hit of $3.3M per season for this year and next, meaning he's not a pure rental, which may appeal to Bergevin even more.
Robidas is an elder statesman at 36 years old, and a former draft pick of the Canadiens way back in 1995. He's yet to score this year, but has 10 assists, 3 on the powerplay. He plays the 3rd most even strength minutes on the Stars' defensive line after Brendan Dillon and Alex Goligoski, and the most minutes on the team overall at 22:22 per game.
Robidas plays a shutdown role for the Stars in the toughest minutes on the team, with the second lowest offensive zone starts among defensemen at 42.8%, and the toughest competition with a 1.518 Corsi Relative Quality of Competition.
Because of that tough minutes role, Robidas has been a negative possession player, but since P.K. Subban and Josh Gorges play that role for the Canadiens, it quite possible that he could get much improved results while playing with Markov.
At 36 years old, with another year left on his deal, Robidas is likely not at his peak value for a trade, and could probably be had for a second round pick and another minor asset. Montreal has three second round picks in the upcoming draft this summer, trading away their own pick seems to me to be a reasonable risk to take on a player of Robidas' calibre.
An even better result of the trade would be that when Diaz is healthy, it pushes Francis Bouillon out of the lineup.