Can a frayed wire cause electronics to drain power faster?

This may be a very stupid question as I don’t understand much about how electricity works.

But my music player is usually good for ~20 hours of audio play at a full charge. Last night using it for 6 hours took about 70-80% of the charge, so something was wrong.

I noticed that the insulated wire near my headphone connector had been split open and some copper wire was exposed. Could that be the reason for the abnormally fast battery drain? (I have no idea how - increased resistance or something maybe? The headphones sounded normal though).

It’s possible that two or more conductors in the headphone cable have come exposed and shorted together, but normally when this happens, the headphones will either cut out entirely or will intermittently pop, sputter or crackle. Otherwise, no, exposed conductors don’t “lose electricity” to the air similar to the manner you’d expect a leaky pipe to. The insulation is just there to keep conductors from contacting one another and, as in the case of high voltages, to keep you from contacting them. Those high-voltage overhead wires you see on tall, steel pylons are uninsulated, in fact.