I have been thinking over the possibilities of how the sole survivor could last 200 years in the vault. I have seen an awful lot of 'cryogenic/cryostasis' theories floating about, but there is one possibility I have not yet seen discussed.
It pretty much harkens back to "The Replicated Man" questline in FO3. Recall how during the discussion with the Dr. Zimmer we learned that some androids were so perfected they did not even realize they were androids? Well, here we are in the home town of the Institute. Why wouldn't it be likely that the sole survivor is actually an android?
We all know that Vault-Tec is a front for crazy over the top human experimentation. Imagine that the Vault is a research facility developing androids and the Vault 111 dwellers are actually gathered as source material for personality templates with which to imprint the manufacture androids?
It would certainly give the Survivor ample motivation to interact with The Railroad and the Institute factions and could lead to some really great end-game plotlines.