A variable pitch prop left to its own devices will move into fine pitch due to the centrifugal twisting moment (CTM). Most S/E aircraft use oil pressure in the hub to increase the blade angle.
With a loss of oil pressure in a S/E aircraft the prop will default to fine pitch, and hopefully you'll be able to generate a bit of power to limp to a field.
Multi-engine aircraft use counterwights or springs so that with the with the loss of oil pressure they default to coarse pitch and feather - minimum drag.