That's up to a player and players agent. Sometimes a player will stay on a teams practice squad instead of signing with a different teams 53 if the current team pays the player the same as an active roster spot. The player/agent may decide that familiarity with the current team and a chance at the 53 the next season is better than taking a chance on a new team. I've seen the Packers do this. But it's up to the player and players agent to give the current team this opportunity. You are right, it's not automatic.