I had this happen two weeks ago (and it's not even the first time). This time I pushed through a cork with its airlock in it.
First, to loosen things up, I put in a couple cups of very hot water and a little Oxiclean, let the cork sit in it for five minutes, then after pouring off the liquid, jiggled the airlock into the neck of the carboy and eased out the airlock with pliers (the airlock is trashed, but so what). Then I took a coathanger, unbent it, doubled the end with pliers, eased it through the cork, let the looped-over section catch on the cork, and gently tugged until the cork came through.
I should add it took a few minutes, but I had already considered replacing the carboy, and after pricing shipping and handling (it's a 3-gallon Better Bottle and I couldn't find one at an LHBS), decided patience and thriftiness would win the day. Next time, I'm going to calibrate my wrists before pushing the cork into the carboy...