What happens when TestFlight app expire?

The next time a user attempts to launch the beta app, they will get a dialog box saying "YOURAPPNAME" Beta Has Expired, and the app will not launch.

The app should not crash (nor run), as your question describes.

You're absolutely right, Toydor!

After the 30-days-period expired, your test won't be able download or run your app. I didn't find a way to extend this period. You only can upload an updated version to get another 30 days.