When I left, I bought my stock options.
I got a friendly letter in the mail a few years later telling me that the company had been restructured, and that my shares are now worthless.
If I'm getting shares as a part of equity, then I'll consider that as part of my comp package...however, if they're stock options, I generally completely disregard them: I haven't yet met a startup to change my mind.
When accepting venture funding, the VC capital will come in as preffered equity which is similar in some ways to permanent debt with no interest payments.
Old company is renamed something like "legacyabc"
A new company is formed with the old company's name. All personnel and IP is moved to the new company", all debt is left in the old company. Original share holders get a big payout.
The old company is now worthless. Shares are now worth less than the original strike price. Original company is likely dissolved.
Bad luck.
Generally you'll have to sign a new contract in the new company to keep working.
If you're really unlucky, your L1 (or w/e) visa is tied to the old company, you now have to leave the country, and can't easily transfer to this new company.
It's a bit weird that you would take wildly different views on the value of one vs the other.
I will now consider negotiating for something like that if I ever again join a startup. Thx!