Lets say, for example, that the grounding electrode on that remote box had a resistance of 25 ohms. Let us further stipulate that the grounding electrode system on the main panel has a resistance of 15 ohms. You get a dead 'hot to ground' short on the remote box, but you don't have any equipment grounding conductor in the feed to the box. Finally, presume that this is a single phase 120V to ground circuit.
Net result: 3A of current flowing through the ground. The remote box is sitting at 75V to ground, and the circuit breaker won't trip. All you've done is created a shock hazard and wasted electricity heating the earth.
Note: 'Resistance to ground' of a grounding electrode is something of a made up number. You presume that the earth as a whole is a perfect conductor, and then attribute any resistance to current flow to the grounding electrode. But in reality the earth is a real conductor with real resistance, and the distance between your electrodes will matter. Imagine that your two electrodes were driven into the ground parallel to each other and 1cm apart. Clearly the resistance between the electrodes will be lower than the overall resistance to earth. But the approximation is good for electrodes spaced significantly greater than their size.