Patrick Chung still has value to this team, it's just a matter of putting him in a position to succeed over being in a position of struggle.
What is Patrick Chung? He is an above average tackle who can lay the wood if needed. He is intelligent, and was set up last year to eventually become the leader of this secondary. He is decent in coverage for about 10-15 yards, but is best utilized in run support or as a support in coverage for intermediate routes. He is a prototypical Strong Safety. With Gregory being down the past few games, Chung has been playing a Free Safety role. That is in stark contrast to his strengths.
What Chung needs is a competent Free Safety to play alongside him so that he can let loose and be the missile he is. If he can have someone like McCourty (or Gregory is he tightens up his play) be able to play deep, and the Patriots can use more Cover 1, man to man, I'm certain Chung will be able to break out again.
Remember Chung in 2010? That's the player who I believe he is. He has just been taken out of position.