circuit breaker that trips when there is a loss of power
A magnetic starter switch or magnetic contactor can do what you want.  Most are designed for fairly heavy loads (8A and up), and they are not consumer-style plug-in devices but rather bulky boxes intended for permanently wiring.  There are circuit breakers with this feature that you can mount in a panel (hopefully you have a panel type that one of these can fit).  The on/off buttons are provided on the breaker itself and/or via a separate switch connected with its own wiring and mounted near the load (usually a machine of some sort).

The Fuji SC-03 is one example of such a circuit breaker: 
 https://www.fujielectric.com/products/mc/mc_ms_tr_sc_neos.html