Well, some relays use very little power, but consider a power FET which need take practically no power at all (down to nanoamps) to be held 'on' depending how you do it.

Or have the logic run on CMOS (4xxx series, good from ~3V to 18V) with a latched output to disable the power to the rest of the circuit, manually resettable.  Look at something like the 4007 + pull-up resistor + P-channel power MOSFET to gate power to the rest of your system.

Microamps should cover that when inactive.

Rgds