So I've been having a hard time finding what the Fuel Cutoff Solenoid does on an Onan (such as my 5500QG HGJAB). The best description I've found to date is:
This is the fuel shut-off solenoid. It is designed to shut off the flow of fuel when the genset shuts down to (1) Prevent backfiring, and (2) Prevent gas from flowing into the crankcase should the float get stuck.
If this is the case, it is almost impossible for it to cause a shutdown problem on a running generator, because the only way the solenoid does anything is when the computer activates it, and if the computer activated it, the shutdown code wouldn't be a 36 (I have no idea what happened but the generator shut down).