Apple, although not a startup, was barely alive in 1997 (ready to default) and became the most valuable company in the world 12+ years later -- worth more in actual profits (never mind stock) than 100 "unicorns" combined...

One might say that Apple didn't so much go from failure to success, as that Apple did fail—rotted from the head—and that, upon its failure, NeXT acquired the "Apple" marque (along with all the employees, factories, and purchase agreements) and rebranded itself using that marque.

Dunno about unicorn, but Brad Feld was an very early Angel investor in Harmonix music systems and they were working for many years before the had breakout success.