You stay for three years. The exit hasn't come yet because the VCs want to see a higher valuation, but the company has grown and the 409(a) valuation is now $5 / share. You've now vested 60,000 options that would cost you $60,000 to exercise, plus you will have an AMT adjustment of $240,000 because of the difference between the strike price and the current 409(a) valuation. So, exercising those options will cost you $120,000 (ballpark, IANA accountant) in exercise cost and taxes.
Keep in mind you've accepted a lower salary for the past three years because of this stock, so you might not have that kind of cash lying around. And even if you do - are you willing to throw $120,000 into a bet that the company will one day have an exit? Keep in mind that the company may have debt, preferred stock, liquidation preferences, etc. and most companies won't share all their past financing terms with ordinary employees, so it may be hard to estimate what a realistic exit even looks like for your stock. And if you're leaving, maybe you're a little disillusioned with how things are going in the first place? You have 90 days to make this decision after leaving the company and then you lose the stock forever.
For many people, the answer at this point is that they don't want to take the bet - and they get screwed out of a large part of what was supposed to be their compensation.
It's a shitty and exploitative system. I worked at a startup where this exact thing happened to many people who contributed immense value to the company. We had a bumpy year, some management turmoil, etc. and many people left before the IPO and got nothing out of their years of hard work other than a shitty, uncompetitive salary. I will never work for another startup under these terms.