Expiring Duty Period
A smart company operations manager would put in place procedures that define actions to take for this, i.e. some type of notification prior to reaching the "maximum" permitted duty day or flight time so that proper decision making can occur so that the mission is not dropped and pilots are not put in a situation where they have to make potentially bad decisions (not saying they would but it's the point of the matter). In the military you have this type of a procedure that helps the commander make a decision on whether the mission is vital enough to continue or whether the mission should be modified. Leaving this until the duty or flight period is about to expire seems ridiculous...but it sounds like that is the norm, unfortunately. As a business owner I would want some say in how this goes down.