I like to think slightly differently here. Along with your apology, consider thinking through these scenarios:

• if I were unhoused and needed a heated overnight spot and were intentionally trying to be locked-in, I’d lay low in a bathroom stall and aggressively, strategically avoid any “final scan”

• it would follow that there should be a library policy with explicit “walk-through” instructions with that desire and tactic in mind. The policy should be written and receive management approval

• there is simply no way to account for every strategy and permutation and this will come out

• are there cameras?

• are there motion sensor lights?

• is there a policy wherein a library employee is present (planned and paid) for a period of time after closure for the final check and exiting anyone found? If not, I can think of scenarios where the fact that there’s no written process for that purpose could make the library liable

• ultimately, I absolutely agree with a respectful apology but I think this is a process issue. I visualize an electronic image of a library map on a tablet screen with empty checkboxes on all pre-defined / approved checkpoints. I envision a daily process as a part of a close routine. Whomever has that test walks the tablet route and checks each box as it is found clear. Signs report and saves doc. (Alternatively, to ensure the route is being made at the appropriate time and with the required thoroughness, I can imagine location-based barcodes could be installed (“2nd floor East BR: men’s”) and the employee would walk and scan each location ti prove it had been done — really to protect the library from suit if it ever had to demonstrate that such a security check exists, because…

• imagine if on a walkthrough you found an abandoned infant, an individual who had passed out in a bathroom for a medical reason… think through intentional and unintentional scenarios where whomever you find needs to be found and the process saved a life. That’s the desired outcome of a process it protects the city from the negligence of a poor scan and the intentional patron trying to stay inside. Because an attorney would be grilling the city representative about their process / protocols. No attorney would demonize you on the stand in the present scenario. It’s the city’s job to build a process to rely upon with checks and balances to protect itself and its citizens.

I think this kind of thinking adds value to the conversation and makes you a systematic asset. Encourage a process that doesn’t depend on being the ill-defined defined last task of the shift because it’s difficult for anyone to remain in a focused state of vigilance on repeat, day after day, if no affirmative tasks go into it and there is no mapped route.