His spirit would have lived on, although I doubt that he would become powerful enough to rival Sauron. He could have had a similar fate where his spirit is cursed to wander the world but unable to take shape again. I don't believe it's clarified anywhere.

Thanks.

What about sauron?

Sauron can regain his power in many ways except for forging rings. It just wont be fun if he is completely vanquished.

I think Sauron is gonna chill w Morgoth in the Void until Dagor Dagorath “the battle of battles” where Morgoth is finally vanquished, along with Sauron I presume. :P

Sauron would "die" in the same sense as Sauruman. His spirit would separate from his body. This had happened to him in the past, but the One Ring hadn't contained the majority of his strength. This is clarified in the chapter: The Last Debate. "If it is destroyed, then he will fall; For he will lose the best part of the strength that was native to him in his beginning, and all that was made or begun with that power will crumble, and he will be maimed forever, becoming a mere spirit of malice that gnaws itself in the shadows, but cannot again grow or take shape"