How to make a push-to-break circuit
A simple way to do this, especially if you're switching 120V, would be to use a relay.  Look for one that is either normally-closed ("NC") or has Form-C contacts.  Form-C combines NO and NC contacts.  Sometimes, in relays, Form-C is called "CO" or "SPDT":



You'll need some power source for the relay coil.  Since this power is getting interrupted by your door contact, make sure it's not hazardous!  Don't have a live 120V contact on the door jamb :)

Then, this is how you would hook it up:



(Sorry for my cheesy drawing!)

This idea could also be used with a solid-state relay, or even a MOSFET, if those would suit your applicaion better.

Good luck!