Vernay muffler about to go?

One side of my original '94 Vernay muffler pulsates or flexes more that the other while the engine is running/idling. When the engine is off, this side feels softer than the other side, and I think I can feel that it is delaminated inside. Do people think that a failure is imminent and it needs to be taken care of right away, or is a failure something more gradual and not catastrophic, and I can wait until it's obviously broken before addressing it? The observer side is the soft side BTW if that makes any difference.