this should be common sense...but if an organism is a unicellular organism it of course would die too, because cells carry out all metabolic processes. The nucleus is the control center of the cell and once that dies the cell will die because it no longer has anything to tell it 'what to do to survive'. It's like a human living without a brain..not possible :( However, normally unicellular cells reproduce rather quickly so chances are it has already made several replications of itself before it's death :)