If you exercise your ISO options (because of option expiration clauses, typically 90 days after you leave a company), but then don't (or can't due to no market for the shares) immediately sell those shares, the spread between the option grant price and the current 409A valuation is due as AMT tax. You have not realized an event where cash is in your pocket, but you still owe tax on the "gain".
You ask what does it matter if the options aren't exercised. Excellent question! It means all that potential compensation you were offered (because you took a lower salary usually in return for options) is now worthless. People don't want to work for free, or have their potential future compensation evaporate.
I see... So what should in theory fix it is if the company granting you the options also provided a guarantee that they will buy shares from you should you be inclined to sell them (A sort of a "sell at current price" option I suppose). This way you can exercise the options, and sell enough shares to cover the tax obligation and hang on to the rest.
Bookmarked to come back later to add detail. There is a better way where your company lets you exercise all your options immediately when you're hired, and you return non-vested shares when you leave.
You ask what does it matter if the options aren't exercised. Excellent question! It means all that potential compensation you were offered (because you took a lower salary usually in return for options) is now worthless. People don't want to work for free, or have their potential future compensation evaporate.