How can a one million megohm resistor be useful?
I used to do periodic maintenance on a detector system for low power
  level particles


Well, the charge on those particles might be the charge on an electron (1.60217662 × 10-19 coulombs) and if there were a 1000 electrons being collected every second the current will be 1.60217662 × 10-16 amps.

Now that is still very small so, if you have a specialist transimpedance amplifier with a feed back resistor of 10\$^{12}\$ ohms, you would generate a voltage signal level of 1.60217662 × 10-4 volts or about 0.16 mV. That is detectable as a signal.

The table below gives an idea about the resistor value needed to be to produce 1 volt for the given current: -



Note, 1 pA is approximately 62 million electrons per second.

I'm thinking of a very sensitive gas-mass-spectrometry here and the ion beam collector circuitry but maybe your machine was something else to do with photon counting?