Quagnoth

Split second doesn't stop triggered abilities from triggering, such as that of Chalice of the Void. If one does, its controller puts it on the stack and chooses targets for it, if any. Those abilities will resolve as normal.

Players still get priority while a card with split second is on the stack; their options are just limited to mana abilities and certain special actions.

If an effect of a spell or ability an opponent controls causes Quagnoth to be discarded, but Quagnoth moves from your hand directly to the Exile zone (due to Leyline of the Void, for example), the ability will trigger from that zone. It will return Quagnoth to your hand from that zone when it resolves.

If Quagnoth is discarded normally (it moves from your hand to your graveyard), its last ability triggers from your graveyard. If Yixlid Jailer is on the battlefield, it won't trigger.

If an effect of a spell or ability an opponent controls causes Quagnoth to be discarded, but Quagnoth leaves its new zone after its ability triggers, the ability will have no effect when it resolves.