Kaz, as you described the situation, it would appear to be less likely to involve a ground loop. You say that the quiet hum is coming from the sub amp(not the driver cone). This would be more likely to indicate a mechanical hum from the sub amp transformer windings(nothing very unusual or to be concerned about as such)rather than an electrical hum caused by a ground loop, coming from the driver cone. If there was a strong enough ground loop current to keep the sub amp "awake", it'd be likely that you wouldn't be asking about a slight hum from the amp which was supposed to be off, but rather a loud hum coming from the cone when the sub was on and playing.
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Enjoy the music, not the equipment.