What is the dual of a diode?
Yes, they are called current regulator diodes. They are essentially a JFET with gate joined internally to source so that you get approximately IDSS for voltages above the pinch-off voltage (and below the breakdown). 

There are much better circuits possible using IC technology, so I think the current regulator diodes are mostly a relic from the past. 

Compare this AL5809 LED regulator IC (two leads) 



Something similar is possible using a three-terminal regulator such as an LM317 and a resistor (resulting in a two lead device). 

It's arguable whether the current regulator diode is actually passive or not, but I'll leave the ontological discussion to others.