The Supreme Court case involves a petition for review concerning the illegal dismissal of Flordeliz Velayo, a former employee of PJ Lhuillier, Inc., who was terminated for alleged misconduct related to a cash overage of 540 pesos. The National Labor Relations Commission ruled that the dismissal was unjust as the misconduct was not serious and the penalties did not align with the nature of the offense, leading to a directive for payment of separation pay and backwages instead of reinstatement due to strained relations. The case emphasizes the importance of proportional punishment in employment terminations and the burden of proof resting on the employer to justify dismissals.