That's an option, but even when the head unit is off, the sub would be powered.
Some time ago I made a 4 stage active sub filter myself, than added a (delayed) remote activated relay and had a print made. If I have to add this detection circuit, that would mean starting from scratch with the whole layout. And it's maybe cheaper to buy a complete amp in the first place. Not as much fun however.

I intend to build the speaker cabinet myself. It's gonne be a well balanced 6th order bandpass design. +110 dB from 60 watts into 8 ohm. No commercial product comes close...

At the moment, the whole project still looks like this:
K.