If an instance disappears, do all previous posts automatically disappear from all other instances?

You can actually see this here; beehaw recently blocked lemmy.world , so as far as Beehaw is aware, lemmy.world "doesn't exist".

• https://beehaw.org/c/lemmyworld@lemmy.world
• https://lemmy.world/c/lemmyworld

As you can see, old posts remain on the instance (unless the admins go and remove them), but new posts don't get received. I think you might be able to post on Beehaw's mirror, but they won't get shared with any other instances.

Of course, this is all subject to change in some future Lemmy version, because this sort of thing can be confusing and counter intuitive.