When building a Twilio application, you can configure fallback URLs to handle scenarios where the initial webhooks fail, such as communication breakdowns between Twilio and your web application. These fallback URLs can be used to define custom behavior in case of errors, including submitting error codes and URLs to Twilio for further processing. To improve the reliability of your application, consider keeping it simple by invoking only minimum required actions, setting up a backup server with static TwiML files, or sending notifications when a request URL fails.