Little Lamplight Caverns is a location in Fallout 3 that is completely populated by children younger then the age of 16.
Little Lamplight was originally founded by a group of Students who, during a school field trip, took refuge in the caverns while the bombs fell on the Capital Wasteland.
The existing rules of Little Lamplight is once a child reaches the age of 16, they are considered a "Mungo"(Adult), and forced to leave Little Lamplight and travel to Big Town, to live out their adult life.
Within the context of the game; very few children make it to Big Town, and don't tend to live long lives if they do make it. There also doesn't appear to be any indication that the adults of Big Town intend on bringing any newborn babies back to Little Lamplight.
Also within the context of the game very few people would know about Little Lamplight and it's residents. Mainly, the residents of Big Town, and the slavers of Paradise Falls.
So how has the population of Little Lamplight been replenished over the 200 years since the war and the original population of children in Little Lamplight?