But it makes sense that the stats aren't changing on a dead character. They were his stats in his last moments of life. A corpse sure ain't got no constitution or wisdom.
That sounds bizarre to me, and could still be abusable. Maybe one should let the own characters die with the headband equipped, revive them without it and hope that the INT 17 is still there... Or imagine Speak with Dead and he is still super intelligent? Where would the line be drawn here?
