Deleting old events can be good customer service.
Have you received inquiries from patrons wanting to attend an event that happened last summer because they stumbled across its page on your website and didn't notice it was dated 2016? It's annoying to click an event link in Google search results and see a "page not found" error when that event has been deleted, but is that worse than a patron mistakenly planning to attend a long-past event?
Deleting old events can be good website maintenance.
Are events from previous years stacking up by the hundreds in the content admin screens of your website? They weren't hurting anyone 1 year after your website migrated to Drupal... but now their vast numbers make it hard to find and maintain permanent pages.
Deleting old events may have no consequences whatsoever.
Are there lots of links to the event on the library's site other than the calendar? That sounds labor intensive and unlikely, right?
Are there lots of links to the event from other sites? (My go-to tool for finding these backlinks is the Moz Open Site Explorer.) It's more likely that other sites link to the library's homepage or calendar than individual event pages.
Did you share website links to events on Facebook a long time ago? My highly un-scientific survey says: no one looks at stuff shared on Facebook from a year ago.
Does Google Analytics show any traffic to the events in the past 6 months? It's worth checking to get a sense of how it compares to overall traffic.
Will there be lots of "Page not found" errors in the website log and Google Search Console? Yes, there will be, until search engines stop re-indexing those pages. Luckily, these errors don't really hurt the library's website.
Any cases where deleting old events may not be a good choice?
Events with repeating dates. You may have some long-running events that were created over a year ago and are still ongoing with upcoming dates. Don't delete those... yet.
You can keep past events on the library's website. Maybe there's no time for this kind of cleanup. But if those old events cause problems for patrons and make maintenance difficult—just like weeding a book collection—don't sweat getting rid of them!