You can exist and be dead, FK. Existence and death are not mutually exclusive. If you are created you exist. If you are given life you live. If you lose it, you still exist but you are no longer alive.
OK, this confirms my original hypothesis. You only consider mortality as regards destination. But if so, then this raises another issue. :) At what point does a mortal soul become immortal? All I know is that you have said it is "by grace" which we must accept. This appears to raise a problem since I think it is the Orthodox view that the vast majority of the saved do not reach theosis during physical life. If that is true, and the immortal soul is determined by accepting grace, then when does this happen? Can a person' mortal soul be transformed into an immortal soul, only to revert back again to a mortal soul?