Please provide Model and Spec for the ONAN.
Do you know how it gets its fuel. Is it direct from the main tank, or tapped into one of the lines feeding the road engine?
Was your gas tank low? Road engine would still run, but gas would slosh away from the genset's pickup.
If you have an ONAN 4KY generator, it probably does NOT have a Low Oil Level switch. It also won't have anything like an Oil Pressure Switch since it's splash lubed. No oil pump, no oil filter. Kinda like a small mower engine.
If God's Your Co-Pilot Move Over, jd
2003 Jayco Escapade 31A on 2002 Ford E450 V10 4R100 218" WB