I was walking through a house during the middle of construction and came across what appears to be a recpticle attached to a pvc pipe that seems to pass a low voltage wire. Also connected to the receptacle was a 14 gauge wire. 
Wiring – Can you identify this receptacle
low-voltagereceptaclewiring
Related Solutions
Yes, that is correct.
Another alternative is to disconnect the existing supply, and run a new line to the switch/receptacle. It really just depends on which line is easier to run.
(Note, I just copied the original image, but didn't erase the ground. The ground should be connected to the box and the ground nut on the receptacle, and switch if it has one. At no point here should the ground be connected to neutral, or anything but a box or a ground screw. Thanks @Skaperen)
You should disconnect the other wire though, at both ends, and connect the conductors together so if anyone mistakenly energizes that line in the future, it will blow the breaker.
Wire gauge requirements may be due to heat dissipation or voltage drop considerations. Standards can impose restrictions that are not really necessary for a particular situation but accommodating those situations would make the standard too complex.
Let us consider the actual heat generated by using a 4 inch #14 pigtail to carry 20 amps. The resistance of 1000 feet of #14 copper wire is 2.525 ohms. 4 inches would have a resistance of 2.525/1000/3 = 8.4e-4 ohms. The voltage drop is 0.0168 volts and the power is 0.34 watts. Double that for the other pigtail and you have 0.68 watts in your box from those pigtails.
By comparison, the resistance of 1000 feet of #12 copper wire is 1.588 ohms. 4 inches would have a resistance of 2.525/1000/3 = 5.29e-4 ohms. The voltage drop is 0.01 volts and the power is 0.21 watts or 0.42 watts total.
The increased heat load is thus 0.68 - 0.42 = 0.26 watts between #12 and #14.
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Best Answer
That appears to be a central vacuum system. The LV wire is to turn the vacuum on via a relay. Hard to tell from the picture if the end of the wire has simply been tucked into the pipe awaiting the final cover-plate install that it will be pulled out and wired to (correct) or if some genius ran the wire inside the vacuum tubing (incorrect.) I would bet on the correct case, though.
The 14 gauge wire would provide AC power for a beater-brush or similar accessory on the vacuum-hose.