Yes, your question is rarely addressed in the spiritual literature, because it is so difficult for the ajnani (un-realized) to grapple with.

As Ramana says, all of the relative forms are impermanent. There is only one thing which does not come and go, which is permanent, and that is the ground of Being, or Source. He says, "Keep attention focused on what is real, what does not come and go, not on what is unreal" (that is, impermanent).

The human body is impermanent. What it (and the entire cosmos) owes its existence to is, as the sutras say, "unchanging," ever-present. Human forms appear and disappear, in limited time and space, within it; but it does not vary in its presence, and is not limited in time or space.

So, the jnani's (realized's) attention is focused on the ultimate Reality, not the short-lived forms through which this Reality merely makes an appearance. Thus the sutras emphasize, "You are not the body."

In specific terms, the jnani (through choiceless awareness) observes changes which are taking place within the organism (and "all things change"), recognizing that a physical body will necessarily follow the course of arriving, remaining, and departing.

You used the word "illness" (as would most persons), but in the sage's mind what is noticed is "change." Change is inevitable; change which eventually leads to death is emphatically inevitable.

The usual human reaction to change, especially when life-threatening, is resistance. For one to whom the self and the Self are one indivisible whole, where is there a basis for resistance?

In Living Nonduality (p. 224: How They Died), I wrote of the "non-resistance to physical death" of four exemplary spiritual teachers: the concluding line speaks about "non-attachment to life itself," that is, to all that is impermanent.

This is--to use your phrase--how sages "look at it when living nonduality."