The designer can design a prop/counter weight/spring/air pressure combination to either run the prop fine or coarse on loss of oil pressure.
As I understood it, generally single engine aircraft run to fine (in order to provide an amount of useful power on failure) whilst multi-engine aircraft run to coarse (to aid feathering).
As a review, the constant-speed propellers on almost all single-engine airplanes are of the non-feathering, oil-pressure-to-increase-pitch design. In this design, increased oil pressure from the propeller governor drives the blade angle towards high pitch, low r.p.m.
In contrast, the constant-speed propellers installed on most multiengine airplanes are full feathering, counterweighted, oil-pressure-to-decrease-pitch designs. In this design, increased oil pressure from the propeller governor drives the blade angle towards low pitch, high r.p.m.—away from the feather blade angle. In effect, the only thing that keeps these propellers from feathering is a constant supply of high pressure engine oil. This is a necessity to enable propeller feathering in the event of a loss of oil pressure or a propeller governor failure.
Learn to fly Airplanes - Propellers