One fairly standard definition for aging is an increase in mortality rate over time. You are said to age if you become increasingly likely to die in any given interval of time. There is an interesting twist, however: researchers have shown that in short-lived species such as flies there appears to be a point in very late life at which mortality rate stops increasing - i.e. aging, by this definition, ceases.
There is some debate as to what this tells us, and how useful in might be in terms of informing aging research or practical applications of biotechnology to extend life. For example, the evidence for any such late-life plateau for mortality rates in humans is tenuous to non-existent. Does it even exist outside very short-lived species?
Here is a further commentary on late-life plateaus in mortality rate and evolutionary considerations of aging:
Too often, aging is thought of as an inevitable accumulation of damage to cells, as something common to all organisms and across all adult ages, or as a physiological process. These ways of thinking about aging limit aging research. We should instead understand aging as an evolutionarily derived condition, dependent entirely on the pattern of the force of natural selection.
In late adult life, the forces of natural selection no longer differentiate between age classes. At these late ages, there is no effective force of natural selection. This leads to a corresponding absence of consistent changes in fecundity and mortality. One prediction of the evolutionary theories is that other fitness characters, such as male virility, should also stabilize in late life. Following the virility of 1000 individual male D. melanogaster, I found that, as expected, male virility also reached a plateau in late life. This result conforms to the predictions of the evolutionary theories of late life.
Late life is therefore a period in which mortality, fecundity, and virility all plateau. ... These results suggest that late life physiology is distinct from that of aging, and that the absence of change in the effective forces of selection in late life, leads to paradoxical transitions in physiology as cohorts enter late life. From these results, I infer that the periods of aging and late life are different physiologically as a result of the very different ways in which they experience selective forces.