Instead, the fifth-year wideout heads into January as a welcomed member of the New England Patriots.
Cut by the Cardinals last month following a December DUI arrest, Floyd played a starring role in Sunday's romp over Miami.
Powering through a flock of Dolphins for a 14-yard touchdown and adding another toe-dragging sideline catch, Floyd furnished Brady with a new element in the passing game -- something plenty of wideouts have failed to do in New England.
"We all know how hard it is to find a role as a receiver in our offense, and we've talked about so many players over the years that haven't been able to accomplish that," Brady said in an exchange that springs to mind the failed Chad Johnson experiment of 2011.
"To come in two weeks after being in the same system for four years, like (Floyd) was, and then come in and play basically the whole game and make play after play ... I think it just gives everyone confidence that he can establish a role for himself and that we can rely and count on him when it matters."
Floyd posted career lows in receptions (33) and yards (446) this season in Arizona, while struggling with drops. Still, this is a player who finished last year with five 100-yard performances over the final eight games.
"He expects you to be exactly where he wants you to be every route. Not a yard off, not a yard too deep, not a yard too short," wideout Brandon LaFell said of Brady in 2014, per the Boston Herald. "He expects you to be exactly where he wants you to be because he's going to put the ball placement exactly right."
As LaFell would tell you, Floyd's early success requires far more than simply jumping into the lineup and making plays.
"First things first, you've got to learn formations. Man, we've got a million formations, and we've got a million personnel groups," said LaFell. "I was just trying to get all that down pat, because at least if I know where I'm lined up, I can kind of figure out what everybody else is doing based on the concept of the play. And second, learning the terms of the plays that we use and different code words we use, because one play I can be the X receiver and if we go to a hurry-up offense, depending on where the ball is spotted, I can be the Z receiver the next play. I have to know the whole play, but first, learning the formations, personnel groups, second, learning the plays and the concepts and just go from there with it."
Offensive coordinator Josh McDaniels noted that Floyd successfully moved around the formation during the Dolphins tilt, saying: "He didn't play the same spot the whole time, which again is a credit to him and the work that he's put in."
Said Brady: "All I know is that he's been working extremely hard every day to get ready to play. He's in there early in the morning and stays late at night. The amount of walkthroughs he's gone through, meetings with coaches and receivers, and how strongly the receivers feel about what he's brought to the room in a short period of time, I just hear nothing but great things."
It's easy to assume that New England can turn anyone into a productive player, but history tells us that plenty of wideouts have come and gone in New England.