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If the final individual experiences an event at $t_1$, the Kaplan–Meier estimator acquires the factor $1-1/1=0$. ThusThe conventional fitted curve is zero thereafter. Its area gives the finite plug-in estimateThe area is a sum of rectangles: if $a_0=0<a_1<\cdots <a_m=t_1$ are the event times, it equals ${\sum }_{j=0}^{m-1}\hat{F}(a_j)(a_{j+1}-a_j)$. Censoring times within a constant segment do not alter its area.

Both terminal estimates have poor reliability because the last risk set has size one: one observed outcome determines whether the entire remaining fitted tail stays positive or collapses to zero. The zero tail is an empirical endpoint convention, not evidence that every future member of the population must fail by $t_1$. With earlier right censoring, the displayed finite area can be especially sensitive to this last event and does not remove uncertainty about the population tail. In the final-censoring case the full mean lacks a determined tail area; in the final-event case the conventional full fitted mean is finite and calculable, but should be reported with this limitation. A restricted mean survival time at a prespecified cutoff within reliable follow-up often avoids the unstable terminal extrapolation.

Let $a_1<a_2<\cdots$ be the distinct observed event times, $r_j$ the risk set size immediately before $a_j$, and $d_j$ the events there. Under independent censoring, the Kaplan–Meier estimator isIt starts at one, jumps down at events, and is unchanged by a pure censoring time; right censoring removes people from subsequent risk sets. If events and censorings coincide, the convention here processes events before censoring, so those censored at the recorded time are included just before the event. The estimated median is the first time the curve reaches or falls below $1/2$. If it never does during observation, the median is not estimable from the observed curve without tail assumptions.

With one remaining individual censored at $t_1$, no event factor is introduced. HenceThis is the terminal observed step value. With an empty risk set after $t_1$, continued horizontal plotting is a convention and supplies no information about the true later survivor function. The tail rests on one person and is imprecise; this is terminal censoring and survival-mean identifiability. If ${\varphi }_0>0$, the unrestricted mean cannot be obtained nonparametrically from this censored tail: extending the last positive step to infinity would give an infinite area, which does not establish an infinite population mean. A restricted mean survival time up to a suitably supported finite cutoff remains estimable.

If the last observed follow-up is a censoring time and the Kaplan–Meier estimator remains positive there, the observed curve does not determine the remaining tail area. Many possible completions give different full means, including finite and infinite ones. A horizontal plotting extension is not proof that the true mean is infinite. If the final risk set is exhausted by events, its Kaplan–Meier estimator factor is zero and the conventional fitted curve has finite area. This includes a unique last individual having an event, but an event tied with terminal censoring can leave a positive fitted survivor value when events are processed before censoring. The random endpoint still does not establish a population support bound. A restricted mean survival time avoids unsupported tail completion.