Zero chance of that happening. First of all, the NFL is a place where QBs get chance after chance (see Christian Hackenberg). But more importantly, Dobbs has played far too well in the preseason to not have any other suitors. In addition, he has pretty tantalizing physical tools. There are some coaches out there who watched his throw against Philly and his runs against the Packers and will say to themsevles, I can make something outta this guy.
There are only 2 possible scenarios:
Scenario 1: Steelers keep Dobbs and he leads them to 4 Super Bowls and goes down as one of (if not) the greatest QB in NFL history
Scenario 2: Steelers trade/release Dobbs, he goes to another team where go goes on to win 4 Super Bowls going down as one of (if not) the greatest QB in NFL history
In scenario 2, the Steelers will also go down as having made the stupidest decision in NFL history for letting future Hall of Fame QB Josh Dobbs go.