Life histories can often be reconstructed from administrative sources and other documents that report specific events, like birth, death, visiting a physician, applying for insurance, or using a service. In a “passive registration” system, individuals are not under continuous surveillance, and subjects are only known to be present when an event occurs. When individuals move out of the registration area without reporting their movements, the censoring times for those life histories are unobserved. This paper describes a new technique for imputing missing exit dates. Our approach uses information from other events (e.g. births, marriages, deaths) affecting the subject and closely related individuals to estimate the distribution of times between last observed events and (unobserved) exits from the registration area. We take into account differences related to age, sex, marital status, and past migration history. The method is tested on data from nineteenth-century Belgium in which exit dates are explicitly reported.