Do no harm to a signal! Does this mean.....

"...Have a set of headphones hooked up..."

It’s the interaction of cables to the amplifiers (amps in source, preamp, loudspeakers, and amp) that make a difference, headphones won’t do it, except to test headphone cables.

"...Isnt this the reason for paying up for cables cause,its so hard to limit signal damage?..."

Audio cables are deliberately designed to change the sound we hear. Common measurements are conductivity, capacitance, impedance, and resistance. Audio cable's job is not to be the perfect conductor, it's job is to improve sonics in a particular way. So some parameters are changed to accomplish this.  

"...BTW it’s cable not wire... Words Count..."

That would depend on the construction of the "cable".  A pair of un-wound wires or ribbons would not be cables.