Use a relay as a resettable fuse?
But the circuit controlled by the relay is isolated from the controlling circuit. A short in the controlled circuit does not necessarily cut power in the circuit which powers the coil which closes the relay contacts.

Even if the relay and the shorted load circuit share the same power supply, there is no guarantee that a short in the load leaves insufficient current for the relay to stay closed.

Of course, circuitry could be added for this. In fact relays are used for protection; for instance in some audio amplifiers, to cut speakers off from the amplifier in case of a fault that places a large DC voltage on the output. Why a relay might be used for this purpose is that it is transparent (does not add distortion to the signal).