Q u o t e: If all of the characters die, obviously the whole hardcore stash will disappear with them.
I don't know how this is an obvious thing. The idea of the a shared stash is that it isn't bound to any character at all, so losing all characters shouldn't result in the loss of the shared stash.
Also, for those who think that it is obvious that the shared stash will or will not harbor both softcore and hardcore items, consider this: disallowing the transfer of the items between softcore and hardcore via the shared stash, but still using the same stash for both. Basically, only softcore characters would be allowed to access any items in the stash that were generated on softcore, and vice versa.