Yeah, you technically need money to buy options, but in most cases you're buying the stock only to immediately sell it again at its current (higher) value. If there's no buyer for your stock you can probably safely let them go, since the market (private as it may be) has determined they're worth nothing.
Not so fast. You also buy stock options when you quit the company, but want to keep the equity you worked 4 years to vest into. Many options plans will require you to buy them within 30-60 days of leaving the company.
For obvious reasons, the majority of options purchase scenarios could fall into this bucket, and not the "sure thing" of selling your in-the-money liquid options after an acquisition.
Another caveat about this is that there are plenty of horror stories about what happened to people with startup common shares that left their company before acquisition. You are, as you probably know if you're been reading here for awhile, last in line in a liquidity event.
