There are a number of reasons why an EMI may no longer qualify as such. This will be due to the occurrence of a "disqualifying event". More information can be found on the HMRC website here.
The most common reason for a disqualifying event is if the option holder is no longer an employee, or ceases to work 75% of their working time for the company.
In this case they have 90 days from the disqualifying event to exercise their options if they want the full EMI beneficial tax treatment to be maintained. They may also want to make an ITEPA 431 election, which will cause a tax liability at that point up to UMV, but any further gain to sale will only be treated as a capital gain.
If they keep the options, but do not choose to exercise them, then any value gain from the time of the disqualifying event to when they actually exercise them will be subject to income tax (and potentially NI as well if they are readily convertible at that point).
Full details on this, complete with example calculations can be found on the HMRC website here.
It should also be noted that the special Capital Gains Tax rate of 10% (Entrepreneurs Relief) associated with shares that have been awarded via an EMI scheme only applies if the sale of the shares occurs at least 24 months after the date of original option grant.