Are there "inverted relays"?
simulate this circuit &ndash; Schematic created using CircuitLab
Figure 1. A typical relay circuit.
How it works:

A control signal, 12 V in Figure 1a, and a small switch is used to power the relay coil.
The relay coil pulls the contact across from the NC (normally closed) contact to the NO (normally open) contact. Mains power can then flow to the lamp.

Alternatively the lamp could be fed from the NC contact as shown in Figure 1b. In this configuration SW1 turning on will turn off the lamp.
When specifying the relay you choose the coil voltage, the contact rating (both voltage rating, current rating and DC or AC) and the contact type - a changeover contact is shown in Figure 1.