How did Danielle survive The Purge in 1992?

She protected herself

Well in fact there were еще survivors than just those three. Kelvin and Radzinsky were in The лебедь which saved them, however Ты cannot forget the rest of the Dharma that was saved. Ben Linus was on the island at that time and he survived it, and so did his father and Alex (Danielle's daughter) too, who was with the Dharma at that time... so we can assume there was some sort of panic room for the Dharma Initiative where a number of them survived. Also, don't forget the "Hostiles" или the "Others" as we know them best, at that time were led by Charles Widmore, Richard Alpert was there too. And they would not have had a secret bunker или anything, so I'm assuming as long as they were a безопасно, сейф distance back from the blast radius they would survive. So I'm assuming that Danielle was also a безопасно, сейф distance away, not to be harmed by The Purge.