That really depends on the engine. Generally, when out of oil, propellers on turbine engines will feather. On most piston airplanes, the default spring loaded position is to low pitch, on the stops. This is not always the case. Some propeller systems will move differently, and some can't be feathered without oil; as oil is used to drive the propeller to feather using an electrical feather pump (hamilton standard hydromatic, for example).
Thanks - It just confirms what I said about shutting the engine down with the S&F while you still have control, as either situation is rather bad.
I'm still surprised that there was no procedure for this, it could catch you out quite badly if you weren't experienced enough to realise what was going to happen and there was no checklist to guide you.