If a start-up terminated an employee, is it required to allow them to exercise the relative portion of their stock option grant that is yet vested?

This is a fairly common question. The short answer is no. But, it depends.

The first thing you should turn to is your grant agreement.  This will explain things like vesting schedules (generally when you can beging exercising stock options, or when you gain access to the stock or cash underlying things like. RSUs.  The vesting schedules may also require that a change in control or IPO take place before any vesting is finalized.

Your agreement is also the most common place to see the details on post-termination grace periods.  This is what may allow you to exercise any vested amounts after you  leave. The rules for these are usually different depending on the type of termination.  Example:  Death or Permanent Disability may give you 6 months or a year, termination without cause may give you 30 days or three months, but being fired or “terminated for cause” often results in an immediate forfeiture of anything vested.  Anything unvested usually is cancelled the date of termination, regardless of the reason.

If your vesting schedule allows exercises and your termination grace period allows exercises, they may still be additional restrictions that would keep you from exercising.  Some of these may be defined in your agreement.  Others may be found in the plan document.

You need to ask the company to put in writing their reasons for not allowing you to exercise.  And you need to do this quickly.  If there is a grace period you don;t want to mess around with the grant after that expires.  If the company is on the edge of a transaction like an acquisition, you don;t want to have to learn a new set of people and rules.