"Thank you all for the input
This house was built about 1940, and had no grounding whatsoever. It is all copper-clad. I was really expecting to have some breakers trip when I put in the new service, but none did. I should have taken a picture of the old 50amp service. I don't know if two rods are required here. The last time I did residential work was 1991. I am a little behind on code, and had I known this is being done, I would have put one in to make sure. I'm not too fond of the connection quality of the standard ground clamps to pipe & rod. I hope in the future there is exothermic welding (cadweld) required. Thinking along those lines....can we reduce the resistance to ground so much that we won't even notice if we lose the neutral to the power company, and have a constant fault?"
In some soil conditions, especially along salt water coast lines, this could happen. Keep in mind that the quality of the grounding at both the source and the load will effect the likelihood of this occurring. One place that this practice is done deliberately is in telegraphic fire alarm signaling. The grounding at each telegraphic transmitter is improved until you can successfully signal via ground return in the event of a break in one side of the circuit.
"This alternating current stuff is just a fad. It is much too dangerous for general use" Thomas Alva Edison