Sure, it's easy. the 555 is triggered by a negative going pulse, so the main thing you need is a common ground and a small capacitor between the 12V rail and the 555's trigger pin.
The power being turned off will generate the negative going pulse.
Note that this assumes there are no capacitors in the 12V circuit that will maintain the voltage across the supply (or limit its rate of fall) after the switch is opened.
This page may help.