relay or switch that remember previous power status after power failure
A latching relay is designed for this very purpose.

"A latching relay is a two-position electrically-actuated switch. It is controlled by two momentary-acting switches or sensors, one that 'sets' the relay, and the other 'resets' the relay. The latching relay maintains its position after the actuating switch has been released, so it performs a basic memory function."

Unlike ordinary relays the latching relay has two sets of coils which move the contacts into one of two positions. In a power outrage they stay in the last position set. 

A simple toggle circuit could be used to enable the use of a single push switch to operate both coils (first push ON (coil 1), second push OFF(coil 2))

e.g. http://www.azatrax.com/latching-relay-circuits.html