Is there such a thing as a pulse relay?
Yes, these are called latching relays as Ignacio Vazquez-Abrams noted in his comment.

From Wikipedia: Relay/Latching Relay


  A latching relay (also called "impulse", "keep", or "stay" relays) maintains either contact position indefinitely without power applied to the coil. The advantage is that one coil consumes power only for an instant while the relay is being switched, and the relay contacts retain this setting across a power outage.