Absolutely! This is something that your lawyers will discuss with you as you move through the litigation process.
If the employee had retained a lawyer, that lawyer likely advised them to keep track of their job search including a log of every interview, follow-up, and any offers received. As the employee is required to keep looking, we can regularly request updates on their mitigation efforts while we negotiate a resolution. If the employee is not making valid efforts to find new work, we will make very clear with their lawyer how that would look to a judge should the matter proceed to litigation.
As a matter of practice, employees are not legally obligated to advise when they have found new work unless it is specifically written in as a condition of their salary continuance. That is why the responsibility is on us to keep asking, and to make sure that you are getting the whole picture before making any decisions.