(see AOD, p.8, FAQ 1.3, p.11)
All enemy figures within 3 spaces of a figure with the Black Curse ability receive -1 Range (Melee attacks still ignore range) and -1 Damage to all attacks they make.
In addition, any enemy figure that deals the killing blow to a figure with Black Curse receives one Curse token. This only takes effect if the figure with Black Curse actually dies (i.e., isn't saved by Undying or a similar ability).
If a Black Curse monster is killed via some indirect means such as Aura, a pit, Burn, or a familiar, who gets the curse?
No one. A “killing blow” must be the product of an attack roll.