Ah no, drow have not lived in shallow caves since the high elves pushed us down into the Underdark. Which depending on historical sources was either two-thousand or ten thousand years ago. For much of my life I was told the second, but now it seems like the first might be true, which meant it was within my mother's living memory... if none others. Our race often does not live much longer than seven or eight centuries and drow elves in particular are likely to die by murder or misadventure during our first.