All,
Thanks for a general explanation of a TIBA. I've never heard the term used before. Based on the information provided in this thread, this is not a procedure used or accepted in the U.S.
In the States, our centers run 24/7/365. They usually work the airspace from 14,000 to FL600. The approach controls work traffic below 14,000. Not all approaches in the States operate 24 hours a day. Except for a few military approaches that close on holidays, the FAA approaches are 7 days a week, 365 days a year.
Getting to the point, in the States, from the time an approach closes until it re-opens, the center having jurisdiction of that airspace will take the airspace and provide services to the aircraft. In the States, 24/7/365, there will be an ATC facility available to provide radar or nonradar services to IFR aircraft, and for VFR aircraft when the controller is able to do so.
If there are any U.S. controllers out there who know differently, please speak up.