Years ago, my neighbor's illegally boosted CB would play thru my speakers. You could hear every word from 2 rooms away. I cannot recall if that happened with my amp powered up.
With my amp off, the woofer creates voltage on the speaker leads as it acts like a microphone.
When the amp is powered up, that voltage disappears.
I would presume the negative feedback from the "noisy" speaker cables attached to the amp output to the "quiet" input causes the amplifier to follow but negate the external voltage.