Regarding what happens with no gas in the tank of a Gen 1 Volt:
Our friend Ari Colin and I have both ended an FMM in our 2012 Volts by running the ICE until the tank is empty and the ICE stops. He does it while parked, to avoid registering any gas miles; I’ve done it while underway. You can’t drive on battery power while the FMM is in progress (forces you to use the old gas), even if it’s fully charged. Once the tank is empty, you regain access to the battery, but in Reduced Propulsion mode, allowing you to drive to a gas pump to get some fresh gas.
There’s a minimum amount you must add to an empty tank to bring an end to the FMM/Reduced Propulsion mode (~1.5 gallons). After you refuel and start the car, the ICE will run briefly to perform a self test, and once the engine starts successfully, will turn itself off and return you to normal operations, allowing you to continue in Electric or Extended Range mode (as described in the manual under the heading, Out of Fuel).
After you run the ICE until it stops itself because you’re "out of gas," a small amount remains in the system. If you fill your Gen 1 tank after running out of gas, as I do in my 2012 Volt, your next FMM will occur ~363 days later. Ari puts into his emptied tank only the bare minimum needed to end the FMM, and his next FMMs tend to be ~318 days later. The difference seems to be because the small amount of "old" gas remaining in the system lowers the "average age" of 1.5 gallons by a few days more than it does the average age of a full tank. Gen 2 gas tanks have a slightly smaller capacity (8.9 vs 9.3 gal), so the effect of residual gas on FMM cycles may vary.
You can also "run out of gas" by driving until your gas gauge reads empty. I drove until the Torque Pro app was reporting "0.0 gals gas / 0.0% tank volume" as I was parked on level ground near the gas pump. The ICE continued to run as I drove the very short distance to the pump, and after adding gas, the engine made no self test upon starting the car. Clearly, the system is not "Out of Fuel" empty when the OBD port first reports the car is out of gas, and, apparently, some gas still remains in the system even after the ICE stops running because the tank is empty.