The break feels thicker than 1/2"; closer to an inch. It goes as far as breaking and loosening that white material I mentioned. For what it's worth, the break/hole is located on a thin wall. Here's what I mean: http://i.imgur.com/5Y9EZ.jpg
So, the break is far enough, that I can feel the other end of that rectangular wall structure (which is part of a closet). I don't know if that changes the method needed to repair it.