Step 2: Carefully Slice It Open
I must emphasize carefully, for it is small and knives tend to slip. My headphone plug was rubber and was fairly easy to cut.
I cut it along the outside seam of the molding. I attempted to avoid cutting the strain relief (the flexible area where most wires break) but the wire appeared to be fused to it and I had to cut that part open as well.
The end was encased in some sort of plastic, I assume similar to hot glue. We will deal with that later.
I chopped off the end about an inch from the source of the problem.