The correct answer is It represents the metric value as NaN to indicate staleness.

Prometheus emits a special sample that has the value NaN to mark that a series has become stale and to signal that the metric is effectively missing for that time range. The NaN marker ensures that graphs show a gap and that query operations treat the data point as absent instead of silently using an old value.

It marks the series with a tombstone and waits for retention policies to drop it is incorrect because tombstones are used when series are explicitly deleted through the deletion API and not for normal exporter stoppage. Automatic staleness does not create tombstones.

It retains the last observed value indefinitely is incorrect because Prometheus does not keep serving the last value when an exporter stops. Instead it inserts the NaN stale marker so that the series is treated as missing rather than presenting a stale constant value.

It immediately removes the time series from the database is incorrect because Prometheus does not instantly delete the series when an exporter disappears. The series metadata and recent samples are retained according to TSDB retention and compaction rules and deletion only occurs by retention expiry or explicit deletion.

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