There are many ways a person could (die) from tiredness, But they would all be accidents. to possibly fall asleep behind the wheel of a car. When we're really tired we can't really think strait, opperating machinery, using a sharp knife or tool, falling asleep in a tub. When we're super tired our judgement can get so impared that we might walk out into traffic thinking the coast is clear! It's a known fact that when we are really tired we will sometimes halucinate.. see things and hear things that aren't real! They will deprive P.O.W's of sleep, keeping them awake for days to get them to break down and give up secrets! Being tired really weakens our mind, and of coarse our body.
But there is no way we can (naturally) die from lack of sleep. When our body and mind are completely exhausted, we will eventually just shut down. Lights out!