It happened to me
This very situation happened to me. Luckily I had another powered sub to swap out with my regular sub and the same thing happened with it. Either sub would come on full blast with a deafening hum, like at 3 a.m., with the receiver off. Frightening as hell. My toddler didn't like it either.
The culprit? There was a crack in the solder in the circuitry where the subwoofer plugs into my receiver. It was fixed within a day, under warranty. No more problems. The receiver (Denon AVR-1603) was only a year old at the time and I never would have suspected this sort of problem with it. But there you go...