When a Tower and the Approach Control closes who takes over the airspace?
All airspace is ultimately owned by some Center (US: ARTCC, ICAO: ACC). Some is delegated to Approach facilities (US: TRACON), and Approach can sub-delegate part of their airspace to a Tower. And Center can delegate airspace directly to Towers without an overlying Approach.
If any facility closes, it’s associated airspace automatically reverts back to whoever had delegated it.