It has built-in functionality for the opening chime, but not for the closing for whatever reason.
I no longer have my elk (sold my house; live in a rental) but I did have code that tracked when doors were opened and closed. I incremented a counter whenever a door was opened, and decremented it whenever the doors closed. For my purposes this was to alert me if any doors were left open for more than 20 seconds (indoor-only animals and kids and contractors that would leave doors open). You could use the same code to play a beep whenever a door closes.
Unfortunately I don't have the exact code... but with some experimentation it wouldn't be hard at all. If you don't want to do it via counters, you can add lines of code for whenever each zone becomes secure again... but it could turn out to be a lot of lines depending on how many zones you have.