If you would write something like: "Bob Hyrule dies of old age", would this work?
Per "Can I increase my lifespan" question: NO!.
In the Death Note, you cannot set the death date longer than the victim’s original life span. Even if the victim’s death is set in the Death Note beyond his/her original life span, the victim will die before the set time.
The only reasonable way for him to die of old age would be if you want him to die of old age within 23 days. This requires him to be very old already.
But the Death Note can only operate within 23 days (in the human calendar). This is called the 23-day rule.
If that is the case, I'm not sure how idiopathic death from old age would present but there doesn't seem to be anything to prevent that "cause".
No, for two reasons:
1) "Old age" is not a cause of death. "Dying of old age" indicates when a person dies from some natural cause.
2) Following #1, you can only specify when a person will die if it's within 23 days.
If you write, "die of disease" for the cause of death, but only write a specific time of death without the actual name of disease, the human will die from an adequate disease. But the Death Note can only operate within 23 days (in the human calendar).
This is called the 23-day rule.
However, the very next rule makes it clear that it's possible to write a cause of death which allows the victim to live much longer than 23 days.
If you write, "die of disease" like before with a specific disease’s name, but without a specific time, if it takes more than 24 days for the human to die the 23-day rule will not take effect and the human will die at an adequate time depending on the disease.
Therefore, you could write someone's name in the Death Note, with the cause of death being a disease that takes decades to develop. This would essentially make the victim immune to the Death Note, while still allowing them to live out a long life (assuming they would have lived a long life anyways).
Keep in mind that this cannot be used to extend someone's life, as the victim will still die at the end of their original lifespan.
In the Death Note, you cannot set the death date longer than the victim’s original life-span. Even if the victim’s death is set in the Death Note beyond his/her original life-span, the victim will die before the set time.