Twilio maintains a redundant, clustered architecture designed to ensure reliable high availability service. This is only half of the challenge. Because of the distributed nature of a Twilio application, your web application must be reliable and highly available as well. To aid you in this task, Twilio allows the configuration of "Fallback" URLs on incoming phone numbers via your Account Portal or the REST API's IncomingPhoneNumbers resource.

A Fallback URL is a URL that Twilio requests in the event of a fatal error while executing your call. If Twilio is unable to retrieve or execute TwiML from your web server, a request is immediately made to the appropriate Fallback URL. Twilio will submit the 'ErrorCode' and 'ErrorUrl' parameters, indicating the error code of the failure and what URL the failure occurred on. You can reply to the fallback URL request with more TwiML, returning a custom application error message, or attempting to recover and continue your call or SMS session.

https://www.twilio.com/docs/availability-reliability