Vein Drinker

When the first ability resolves, if the targeted creature is no longer on the battlefield, the ability doesn't resolve for having no legal targets. No damage is dealt.

When the first ability resolves, if the targeted creature is still on the battlefield but Vein Drinker is not, Vein Drinker will still deal damage equal to its power as it last existed on the battlefield to the targeted creature.

Each time a creature is put into a graveyard from the battlefield, check whether Vein Drinker had dealt damage to it at any time during that turn. If so, Vein Drinker's third ability will trigger. It doesn't matter whether the damage was combat damage or not. It also doesn't matter who controlled the creature or whose graveyard it was put into.