I can't see how just leaving the tuner on but not have the amp running will break in the cable. It will not be performing any function will it?George (Xti16) is correct, Stan. The input of the amp will "look" essentially the same to the cable and to the tuner whether the amp is on or off. The amp's input impedance, and therefore the amount of current that is drawn through the cable from the tuner, will usually be determined to a close approximation by a resistor (perhaps 47K ohms for a typical unbalanced input) that is connected between the amp's input terminal and ground.
Disclaimer: No opinion about the value of break-in is expressed or implied in this response :-)
Best regards,
-- Al