It depends on the relay for a simple SPDT relay it doesn't matter.
I know that there are latching relays which have a permanent magnet so if power is applied in one direction, the relay turns on, if it's applied in the other direction, it turns off.
It wouldn't surprise me if you can buy a SPDT relay which has neither contact connected when no power is applied to the coil and a different contact is connected depending on the direction of the current applied to the coil.