Can an unused cable break in?

Yay! So there is a circuit. Like I said. Only for some reason me saying it triggers terminal butt-hurt, the cry-bully has the post removed. I try to not get in his head, but somehow keep getting sucked in. Must be the vacuum?

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.

No, that isn't why it works. And it doesn't measure voltage, but merely detects it. No offense but mainly what I detect is word games. Someone says something and whether totally correct or incorrect means nothing but an opportunity to interject.   

Nothing burns in without current. End of story.

One of the things that is different about power cords vs ICs and speaker cables is there is always voltage present as long as power is supplied whether or not the device is turned on. If the dielectric is the primary thing that burns in, it seems to me it is the capacitive property of the cable that is affected and current shouldn't matter. What say ye?

I say ye R OTL. A medieval term invented by the Duke of Sandwich meaning "out to lunch": not all there.    

Voltage is a differential. It is in other words measured between two things. Across a circuit. Without which (a complete circuit) there is no voltage, no amperage, no capacitance, no nothing. (Try buying a meter that can read voltage, resistance, capacitance, inductance- you name it - without being connected to anything.) 

Yet another way to think of it, your imaginary voltage, which of the conductors is it "on"? A 120V circuit (there's that word again!) consists of one black "hot" wire and one white neutral wire. Normally voltage is measured across the black and white. But there is in principle no reason it cannot be measured across black and ground. Same 120V either way. But what about white/neutral to ground? Where is your 120V? Not there! So where is the voltage? Not there.  

I agree with Millercarbon's comment about 'burning' in. In my 12 years or so of playing I have always noticed (almost always) that changing gear, cords, interconnects, etc. needs to settle in for several hours if not days to calm or whatever you want to call it. 

I call it settling in, so as to distinguish it from burning in, warming up, and reaching saturation or equilibrium.

Burning in happens only once, when something is brand new. 

Settling in happens every time after something like a cable is disturbed. The more it is bent, twisted, banged around and exposed to temperature extremes the greater the difference and the longer settling in can take. This is why a cable used even for years can sound awful after shipping. Discovered quite by accident when two identical power cords were swapped. Each time the one going in sounded worse than the one coming out- but only for some minutes, after which it sounded the same. In this case settling in took only a few minutes. After shipping it could be hours.  

Warming up happens every time after something is turned off. How long it takes to warm up is totally arbitrary, because it is pretty much open-ended. The longer it is left on and running the closer it gets to saturation or equilibrium, the point at which it is pretty much done changing.  

The reason for "pretty much" is this phase lasts for hours, long enough for sound quality changes to start being affected by AC power and other daily noise cycles. 

Not that everyone will hear or notice all this. But to the extent you are at least aware this is what is going on this awareness greatly improves your odds of being able to hear it when you come across it. 

So we still don't know, and fall back on: Any current however small and it is burning in.

No current and no it will not be burning in.  

It is far from clear from your writing but it seems to me that what improved was the transport. We just can’t tell. For example, you’re asking if it improved while unused- while at the same time saying it was plugged in. Well, if it was plugged in and turned on then it was not unused. If it was plugged in and turned on then both the cable and the transport were burning in the whole time. So it could be the transport, or the cable, or both.

This is something I have known for a very long time, that was recently confirmed talking with Ted Denney. He said it is dielectrics, the insulation around the wires, that takes a long time to soak and reach equilibrium. That is mainly what is happening with burn-in. This happens at about the same rate whether playing music or just idle. As long as it is on with current running in it, even at a very low level, it is burning in.    

Oh fyi, he said about a week of being turned on, 24/7.