Regardless of the efforts of managers/supervisors to do the right thing and behave in ethical ways, they make mistakes, and their subsequent apologies may have implications for the well-being of their colleagues/employees and themselves. Dr. Kathryne Dupré and her colleagues explored this issue and found that following different types of transgressions, manager/supervisor apologies were positively associated with the psychological well-being and emotional health of their colleagues/employees, and further, that the apologies of managers/supervisors were positively associated with their own psychological well-being, emotional health and authentic pride. It seems that when managers/supervisors apologize for wrongdoing it makes managers/supervisors and their colleagues/employees feel better about transgressions, and subsequently feel better themselves.
You can read this article here: https://link.springer.com/article/10.1007/s10551-013-1685-3, or another story about this here: https://www.psychologytoday.com/hk/blog/fulfillment-any-age/201406/4-ways-make-better-apology?collection=153137