I have asked and seen asked about how special initiative works and gotten these responses:
-When you are being removed and losing the battle, Special Initiative takes place during the state of the battle when you were being removed (this answer allows for using Foreign Sword to negate Unholy Writ).
-Special initiative happens when you are being removed from battle, but you can only target cards that are now targetable unless they are Enhancements from battle (so you can negate Achan's Sin, but not Unholy Writ because nothing targets Discarded artifacts and only "negate last" on Herod's Treachery).
-Special initiative happens when you are being removed from battle, but you can only target cards that are now targetable unless they are Enhancements (so you can negate Achan's Sin and Herod's Treachery with any regular negate, but not Unholy Writ).
They are somewhat nuanced, but can make a very big difference.