The latest example is outfielder Melky Cabrera, whom the Blue Jays inked to a $16 million, two-year deal to patrol left field and add another dimension to the newly revamped lineup.
Cabrera was enjoying a career season with the Giants last year, but he tested positive for testosterone a little more than a month after winning the All-Star Game MVP Award, and therefore served a season-ending 50-game suspension.
"We did a lot of work on him. Obviously, with the suspension, that was something that was very important to look into," Anthopoulos said during a news conference on Tuesday morning at Rogers Centre. [We] talked to a lot of teams that he was on -- front office, teammates, staff -- everyone had great things to say about him. Obviously, no one would condone what happened, what he did.
"Those are questions that I had when we were negotiating with him, and I was satisfied with the answers."
Though Cabrera's failed test may ultimately hang over his head for the rest of his career, Anthopoulos feels comfortable being the one to grant him another shot.
"The thought right now would be that [during] Spring Training it will be addressed once, and that will be the end of it and we'll turn the page," Anthopoulos said. "We asked those questions, that was part of it. There have been a lot of players in this game that have gotten a second chance.
"Again, no one condones it, but people have been given a second chance, and we did as much work as we could on the player."
Cabrera, who was left off the Giants' postseason roster, was leading the National League with a .346 average at the time of his suspension, as well as 11 homers, 60 RBIs and a career-high .906 OPS.
Although Cabrera was eligible to return during the playoffs, San Francisco chose to continue without him. Reports surfaced that he never reached out to his teammates after the suspension, and he has since remained quiet, but Anthopoulos has no concerns about his character.
After doing his due diligence and having several talks with others around the league about Cabrera, Anthopoulos came to the conclusion that the 28-year-old is not only a good fit from a talent perspective, he'll make a positive impact in the Blue Jays' clubhouse.
"We obviously think he can help us win games. More importantly, we've heard he is actually a great teammate, he's a great guy," Anthopoulos said. "Obviously, he made a terrible mistake. ... But I've said this before, we will give someone a second chance. I don't think you will see us give guys a third or fourth."
Cabrera may come with baggage, but questions also surrounded fan favorites Brett Lawrie and Colby Rasmus when the Blue Jays acquired them, and both transactions have worked out well.
Cabrera will be joining Rasmus and three-time All-Star Jose Bautista to form a dynamic outfield. Cabrera will be the everyday left fielder; newly appointed skipper John Gibbons, who has a history with Cabrera from their days together in Kansas City, envisions him hitting in front of Bautista and slugger Edwin Encarnacion.
"I like Melky at the top of the order. He's such a good hitter, he gets a lot of hits. You could hit him in the middle and he will drive in runs," Gibbons said at his introductory news conference.
"I think he fits there [at the top]. It's too early to say who's going to hit where. Alex paid a lot of money to get him to come over and hit, so we want to get him as many at-bats as we can."
Gibbons, who managed the Blue Jays from 2004 to 2008, became a Cabrera fan during the switch-hitter's lone year with the Royals, 2011, when Gibbons was the bench coach. He described Cabrera as someone who brings a lot of energy to the park and a player fans will be quick to embrace.
"He's smiling all the time, he brings it, and he's a good player, a real good hitter," Gibbons said. "It's unfortunate what happened, but he's still a good hitter.
"Fans are going to fall in love with him -- the way he approaches, the way he shows up every day to play. And you know what? He's pretty darn good."
The signing of Cabrera lets the Blue Jays employ speedster Rajai Davis as a fourth outfielder and late-game pinch-runner while allowing 22-year-old Anthony Gose more time to develop at Triple-A Buffalo.
Cabrera, an eight-year veteran, spent time with the Yankees and Braves in addition to the Royals and Giants. He's a .284 career hitter with 84 stolen bases and 69 home runs. Over his last two seasons combined, he has been worth 8.8 wins above replacement, according to fangraphs.com.
Chris Toman is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.