According to ICAO Annex 2, after landing the pilot should give an arrival report to the appropriate air traffic services (ATS) unit at the arrival aerodrome in order to close their flight plan, unless otherwise prescribed by the appropriate ATS authority. In other words, the flight plans do NOT close automatically unless otherwise prescribed by the appropriate ATS authority.

• After landing to an uncontrolled airfield the pilot should close their flight plan by giving an arrival report to the nearest ATS unit, unless otherwise prescribed by the appropriate ATS authority.

If the pilot fails to close a flight plan within 30 minutes of the estimated time of arrival, the responsible ATS unit will not be aware of the arrival and will consider that the aircraft is in an uncertainty phase (Source: ICAO Annex 11).

Aerodrome operators do NOT manage flight plans — only ATS units do.

ICAO Annex 2
3.3.5 Closing a flight plan

3.3.5.1 Unless otherwise prescribed by the appropriate ATS authority, a report of arrival shall be made in person, by radiotelephony or via data link at the earliest possible moment after landing, to the appropriate air traffic services unit at the arrival aerodrome, by any flight for which a flight plan has been submitted covering the entire flight or the remaining portion of a flight to the destination aerodrome.

3.3.5.3 When no air traffic services unit exists at the arrival aerodrome, the arrival report, when required, shall be made as soon as practicable after landing and by the quickest means available to the nearest air traffic services unit.