Can an unused cable break in?

MC, the parasitics complete the circuit. There are effectively small distributed capacitors along the length of the cable from line to neutral, line to ground, and neutral to ground. For a 2m power cable I would guess these would be in the neighborhood of hundreds of pfs.

My serious question still is as long as the cable is plugged in to AC, and these parasitic capacitors (caused by the insulating material as well as the cable geometry) are being charged and discharged why would the component need to be turned on in order to break in the cable? This is assuming the dielectric is the primary reason for the break in.

If a large current is required is required to break in a power cable it suggests a more complex reason for break in, perhaps one involving the metallurgy of the wire.

Many components cannot be turned off; the off switch merely puts it in standby mode. As long as the PC is plugged into a live wall socket and the device, there will be current flowing. Hence, it will burn in even with the CD player “turned off”. 

In addition, if the PC has capacitance across the individual conductors, the cable will be able to achieve some break in even without it being plugged into a component. It only needs be plugged into a live outlet. Most PCs do have capacitance across its conductors.

Off is off. No current when off. Zero. None. Nada. Zip. It is the very definition of OFF. Off in other words means off.

Now if you want to redefine off as some lesser but still non-zero amount of current is flowing through a closed- not open, closed- circuit, well then you can call it "parasitical" or "not on" but you cannot call it "off" as otherwise you have so destroyed the meaning of the word it loses all utility.

Use your words. Don't suck the life out of them. Don't be a parasite.

A cable is not a horse :)