...when will a being count as dead?
In the current setting, under most circumstances, when their original body dies. Under certain circumstances it may be possible to "die" again if the soul is given a new body; to what degree these are bugs, "happy accidents" to be Bob Ross about it, or WAI is not always clear.
In the future, this will be determined by what the world settings and myth generator have created. In some worlds souls may be immutable things, that occasionally inhabit mortal forms. In others, souls may be immediately yanked to an appropriate afterlife, and ghosts are merely false shadows. In yet others, it might be something more Egyptian; with the Jb (heart), Sheut (shadow), Ren (name), Ba (personality), Ka (vital spark), Khat (physical body), and Akh (magical drive) all being distinct parts of what makes a "person", with different roles to perform as you go through the stages of life and death. For instance, ordinary (first) death was when the Khat (physical body) failed, and the Ka (vital spark) left it; with the proper rituals, the Ba (personality) could also be freed from the Khat, to be rejoined with the Ka so it could live on (in a way) as the Akh.
This is but one very simple example of a historical treatment that would be one of perhaps billions of different variants of how cosmology works that the myth generator could come up with.
Will beings whose souls reside in items die when the item is destroyed?[/color]
This is entirely dependent on what sort of myth has been generated for that world. Souls might be immutable things more-or-less free to choose destinations; they might be fragile things easily broken and dispersed (or eaten!), they might be durable but subject to moral forces beyond their strength... procedurally generated mythologies will allow all sorts of awesome things that we've not even thought of yet. Think about all the ways to handle such things that have existed in any real-world or fictional mythology, and then remember that's only a tiny spec in the corner of the possibility space. (Yes, this is going to result in some really amusing "Is this a bug or just the way the universe works?!?" threads.)