This question is inspired by another thread:
http://boards.straightdope.com/sdmb/showthread.php?t=659560
–but deals with a somewhat different scenario. As opposed to simply not having a copy of one’s birth registration, what happens to someone in a modern, industrialized society whose birth wasn’t officially registered at all? Some people born as late as the 1930s in isolated areas of Appalachia or the rural South apparently never had their birth officially recorded by the government. In at least one case, a man born in southeastern Kentucky around 1937, it prevented him from getting a passport, even though he had obtained a delayed birth certificate some years earlier in order to qualify for Social Security:
http://www.journalgazette.net/apps/pbcs.dll/article?AID=/20070821/LOCAL0201/708210312/1002/local
Lacking any form of a government birth record (other than perhaps baptism, if the church was a state church) was, of course, the norm prior to the mid-19th century. For that matter, many Americans born even in the early 20th century also lacked state-issued documentation of their date and place of birth, but usually they managed to obtain passports, drivers’ licenses, Social Security benefits and the like without trouble. As those generations disappear, and as lacking a birth certificate becomes more and more of an anomaly in Western countries, things inevitably get tougher for people born in circumstances that precluded or placed little value on having births registered.
What about someone who couldn’t even scrape up enough evidence to get a delayed birth certificate? In other words, there are no living people who witnessed the birth, no newspaper announcement of the birth, no baptism, no supporting documents that anyone can find to verify that the person was born in a given country and is a given age. Would they become sort of de facto stateless?