The classic 1N34A Ge Diode has a Vf of 1V... how could a diode with such a high Vf work in crystal sets they were packaged in?
It lists Vf as 1V at 5mA


It's never this black or white: -



All diodes have a VI relationship that is non-linear in their forward conduction area and will never have a boundary where they conduct/non-conduct. Look at the graph above - with 100 uA flowing I bet the forward volt drop is probably 0.1 volts. Look at this one: -



For the 1N34A (green) the volt drop is about 50 mV with 30 uA flowing.