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: 
The vocal track, particularly if it is just one singer, is usually found in the centre. This means it is mixed equally into left and right.

If you produce a difference signal, L-R or R-L, then this common mode material (anything mixed in equal proportions to left and right) will be attenuated.

Such a situation can happen in headphones if you break the ground connection.

Note that the headphone jack has only three conductors (tip, ring, sleeve). So the headphones share a common return path, or ground.

If this ground is not properly connected to the player, it still remains properly connected to both headphones through the jack. The headphones then form a series circuit: left amplifier output, left headphone, common ground, right headphone, right amplifier output.

What you're hearing in the headphones then is the voltage difference between the amps. Any component of the signal which is common mode (mixed into both channels equally) is suppressed. (If the amplifiers produced exactly the same signal, then the difference would be zero!)

So vocals in the center, and other things that are panned in the center such as (typically) bass guitar and kick drum, are faintly audible or not at all.

You hear a signal that lacks bass and in which the vocals are faint and distant. 

But the reverb on the vocals may sound huge, because it is a stereo effect with a differing left and right signal! It may sound like the reverb mix is much more "wet" with respect to a tiny "dry" vocal signal.

Additional notes:

Why can the amplifiers work without a ground? Because each amplifier can regard the other as a ground, so to speak. A voltage amplifier has a low output impedance. One amplifier's output can serve as the ground or return path for another amplifier's output and vice versa. This is the basis for amplifier bridging. The main point is that the connection from one amplifier to the other is a complete circuit; lifting the headphone ground does not interrupt the circuit.

This type of connection between two amplifiers is exploited to bring about *bridging*. But bridging requires that one of the amplifiers receives an inverted signal, so that their difference is really addition! Bridging is a technique of using two weaker amplifiers to make a single more powerful amplifier. Bridging also allows an amplifier to be DC-coupled to the speaker, even if it is based on a single voltage supply (meaning that no coupling capacitor is required in series with the speaker to block DC). The technique is used in some small audio amplifier IC's that run off a single supply, but in the pro audio world, large stereo amplifiers sometimes support a bridging configuration. An important parameter of a stereo amp (to some users) is whether or not it can be easily "bridged mono" for more power, or driving of smaller impedance loads. So, what you've done with your jack is essentially bridged the left and right amps, except they have somewhat different signals, and one is not inverted with respect to the other!
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.