Can you respond to Necrologia with damage to kill players before the effect resolves?

Example: A player on 40 life casts [[Necrologia]], announcing that they will pay 39 life and draw 39 cards. In response, can you ping that player for 1 damage, and then they kill themselves by paying the 39 life? Or does the resolution fizzle because they no can no longer pay the cost? Or can they change the amount of life they choose to pay as the effect resolves?

Many thanks.