I was just in a jigoku game and my opponent, at 3 honor, played assassinate and immediately lost. He was thinking he could use duty to prevent the honor loss. Is this correct and jigoku had a bug or otherwise didnt work properly, or can you not use duty in that case (and if so, why)?

Interrupt: When the effect of a card ability, ring effect, or framework step would cause you to lose your last honor – cancel that effect, then gain 1 honor.

Key word is "effect".

The honor loss from Assassination is a cost.