Do not rely on the printed date alone. TN workers may qualify for the limited discretionary grace period after employment ends, bounded by their remaining authorized validity. Have counsel review the actual end date and status history promptly; the grace period is not permission to start another job.
Separate the authorized period from the authorized activity
Bring the termination terms, I-94 and any prior use of a grace period within the current authorized validity period to the review. Discuss a new qualifying employment arrangement, an eligible change or extension request, or departure. Job-search planning and actually performing work are different questions.
Confirm the permissible sequence before acting on a new offer. What settles this in practice is the pairing of two documents: the employer letter fixing the last day of professional duties, and the admission record showing the authorized period. Where they conflict with a manager's recollection, the written records govern.
Note also that any applicable grace provision is discretionary and bounded by whatever remains of the authorized validity, so a long period printed on the I-94 does not translate into a long cushion. Before acting on a new offer, a useful test is to put three narrow questions to counsel: whether the person may remain, whether the person may work, and whether the new employer's filing must be adjudicated before any duties begin. Those are three separate answers, and only the third depends on the new employer.