Bob (Gdnrbob), thank you kindly.
What the OP has described isn’t surprising. The 2Wq has a very high input impedance, described as being more than 100K. When the amp that is driving it is turned off the high impedance input is left in an essentially uncontrolled state, referred to by EE’s as a "floating" state, but with the ground connection to the amp still being present. That amounts to an invitation to hum problems.
The sub is plugged into its own electric socket.
If practical, it might be worth trying plugging the sub and the amp into the same outlet. Assuming that doesn’t help, though, and if you’d prefer to not keep both components turned on all the time, what I suspect will help is as follows:
Purchase two resistors having a resistance of approximately 1500 ohms or so (the exact value isn’t critical; anything between about 1000 and 2000 ohms should be suitable), and a power rating of at least 2 watts (that rating assumes the resistance is at least 1000 ohms, and takes into account the power capability of your NAD 375BEE). Connect one resistor between the + and - terminals of the sub’s input for one channel, and the other resistor between the + and - terminals of the sub’s input for the other channel.
You may be able to find suitable resistors at Radio Shack, or if not you can order them from an industrial electronics distributor such as Digikey.com (which has no minimum order requirement or handling fee), mouser.com, or newark.com.
The quality of the resistors is not critical, and I would not expect them to have any impact on sonics.
Regards,
-- Al