Yes. In employment cases, you must make a good faith effort to reduce the money that you have lost in wages because your former employer caused you to lose your job. As a discharged worker, you have two obligations:
to make reasonable efforts to find employment; and,
to accept employment of a 'like nature,' if offered.
If the other side can convince the judge or jury that you did not do what was reasonable, you could win your case, but still be awarded only one dollar (called nominal damages). However, if you did reasonably look for other work, you will not be denied damages for lost wages just because your efforts were unsuccessful and even if your efforts could have been more exhaustive.