No player with actual value would get screwed over. You're either going to be brought on to a team or you're not.
Very few players with actual value are cut. The only exception are the players with huge contracts, but those players got the bulk of their money upfront.
You are thinking about this from the team-who-needs-players standpoint, not the players. The better players wouldn't mind teams cutting them, especially in the last 2 years of a contract because by then, they've got most of their money from that last contract and signing a new contract would give them a fresh signing bonus that would exceed their previous team's salary for the season.
Scandrick is a perfect example. He may love playing for the Cowboys, but he would be perfectly happy money-wise if they cut him before the season started, even at the last moment. That's not happening of course because he's one of our best defensive players, but he got his upfront money so he's on the tail-end of a contract, which means getting a new contract with anyone else would pay him more in 2015 than he will make with Dallas.