Not just departures. Assume an emergency takes place en route, and that airport with the closed runway is the only one available within a big area. What now?
There are two things to distinguish:
- Operating hours
- Temporary surface (runway) closure
If the airport is already 24/7, the tower will remain staffed.
If not, once the airport closes on schedule, the airspace classification changes from controlled to uncontrolled. This has nothing to do with the runway's status, NOTAM does:
Closure = NOTAM
Surface closure must be NOTAMed. So that the flight crew are made aware of such limitation. A similar limitation applies to taking off in white-out conditions, where a return may not be feasible.
Check your national authority's documentation for NOTAMs, for example for the FAA it will be AC 150/5200-28F. NOTAM issuing for your example is the airport management's responsibility.
! JFK JFK RWY 12/30 CLSD DLY 1400-0100
In the above example runway 12/30 will be closed daily from 2 pm to 1 am – irrespective of when was the last departure.
From ICAO Doc 4444, 188.8.131.52.3.4 states that for properly arranged construction/maintenance work, those carrying out the work are not required to have two-way communication with the tower. 7.5.3 confirms that such work affecting a runway shall be communicated via NOTAM, ATIS, and applicable visual signs (e.g., a large erected illuminated X sign).
By checking the NOTAMs, the flight planners/crews will know if they need to plan for a takeoff alternate (instead of a return to the departure aerodrome). That requires a known distance (wind and ISA deviation accounted for) to that alternate based on the aircraft and number of engines. Otherwise the flight will be cancelled (good news for you).