What happens when a propeller is placed in beta while feathered?
Depends on they type of turboprop engine.  With a straight shaft turboprop engine like a Garrett TPE331, this is not possible as feathering the props are controlled by the conditioning levers and also shut down the engines in the process.  A free turbine turboprop would allow a person to feather the engines and then pull the power levers to the reverse position.  Note that the propeller lever control does not set beta here, rather the power levers do, moving from idle to beta to reverse.