If the FAA is deemed to not be equivalent anymore to the local air-safety regulators, planes from US-based companies will stop being allowed to fly in the airspace of other countries and planes made in America will not be certified for flying in that airspace or being purchased by companies in those countries until fully checked (at great cost) by a certification authority under the regulatory oversight of a local regulator or one deemed equivalent.
This will quite likely start by the EASA (European Air Safety Agency) not accepting FAA as an equivalent regulator anymore.