In general terms, for group medical insurance, when is an employee considered to be an "inactive employee"?

If an employee has been terminated but is still receiving vacation pay during a period following termination, is the employee "inactive"?

Check with your group contract. It should specify last day of employment or end of the month after termination. If it doesn't specifically indicate anything in the contract go with how you would treat an employee who didn't have any vacation time and was terminated. Some companies continue benefits until the end of the month while others cut them off right away. Paying an employee vacation time after termination is more of a serverance kind of thing and should not keep the employee active beyond the termination date.

I am curious... why is there a concern for "inactive" employees?

Usually I find that "inactive" relates to being on an unplanned leave of absence or extended leave related to FMLA etc. Terminated usually means no longer employed and no longer on the payroll, any payments due for structured severance, vacation etc is usually an Accounts Payable item not a Payroll item.