At the high level aging is defined as an increase in mortality rate with time due to intrinsic causes. By this definition some species become "immortal" in old age: their mortality rates grow to become high but then cease to rise further in the final stage of life. The best data for this effect has been gathered in flies, and a lot of theorizing has taken place on what this might mean for the evolution of aging.
Finding this same effect in humans is a more challenging undertaking, as the data for human aging in extreme old age is sparse. The number crunching to date has leaned strongly towards there being no slowing of the increase in mortality rate over time in humans, and certainly no late life mortality plateau of the sort that occurs in flies. Here is a recent publication on this topic:
The growing number of persons living beyond age 80 underscores the need for accurate measurement of mortality at advanced ages and understanding the old-age mortality trajectories. It is believed that exponential growth of mortality with age (Gompertz law) is followed by a period of deceleration, with slower rates of mortality increase at older ages. This pattern of mortality deceleration is traditionally described by the logistic (Kannisto) model, which is considered as an alternative to the Gompertz model.
Mortality deceleration was observed for many invertebrate species, but the evidence for mammals is controversial. We compared the performance (goodness-of-fit) of two competing models - the Gompertz model and the logistic (Kannisto) model using data for three mammalian species: 22 birth cohorts of U.S. men and women, eight cohorts of laboratory mice, and 10 cohorts of laboratory rats. For all three mammalian species, the Gompertz model fits mortality data significantly better than the "mortality deceleration" Kannisto model (according to the Akaike's information criterion as the goodness-of-fit measure). These results suggest that mortality deceleration at advanced ages is not a universal phenomenon, and survival of mammalian species follows the Gompertz law up to very old ages.