Subwoofer hums when plugged in and connected to amp, even if amp is unplugged

The subwoofer in question is the built-in powered sub in one of my Vandersteen Quatro loudspeakers. The speaker takes four high-level inputs, two for tweeter/midrange and two for bass. The hum occurs if the power cord for the subwoofer amp is connected and either of the two bass section inputs is connected (could be positive, negative, or both). The hum is present if the source amplifier is on or off, and is present even if the source amplifier is unplugged!

Why would a hum occur if a single terminal is connected to an amplifier that isn't plugged in?

I've tried a ground lifer, no change. The other Quatro does not have this issue, and they are plugged in to the same outlet.