Question: Every once in a while, my eighth-inch audio jack will slip loose and I'll seemingly lose only the voice part of a track -- leaving somewhat of a "karaoke" version. What I would guess about how audio plugs work suggests that I'd be making this up; however, I've asked and others tell me they've experienced this as well.

What causes this stripped vocals from audio when a 1/8" audio jack is partially unplugged?

Answer: 
When the plug starts to slip out of the jack, very often it's the ground contact (sleeve) that breaks its connection first, leaving the two "hot" leads (left and right, tip and ring) still connected.

With the ground open like this, both earpieces still get a signal, but now it's the "difference" signal between the left and right channels; any signal that is in-phase in both channels cancels out.

Recording engineers tend to place the lead vocal signal right in the middle of the stereo image, so that's just one example of an in-phase signal that disappears when you're listening to the difference signal.
If you look carefully at the jackplug, you'll likely see three (or more) contacts. These are ground (shared), left and right.

I would guess that the vocals are on only one of the stereo tracks (ie. left or right but not both). When the plug comes partially out, you're getting mono.