What does a customer in a country where there is no apple shop or authorized apple service do when the Face ID doesn’t work?

Take the phone to the country you purchased the phone if there is no Apple Store or Authorized Service Provider. Maybe owning an iPhone is not the best option for you. Buy a phone which can be serviced in your country.

In every country Apple actually does business in and sells iPhones, there are either Apple Service Centers or Apple Authourzed service centers (in some countries, only the supported carriers are authorized service providers, e.g. most African nations the carrier provides technical support and service).

If you’re in a country with truly no Apple Authorized iPhone service providers, you’re in a country where Apple does not actually do business. In such countries, there is no support, of any kind (e.g. Iran, Syria, North Korea).

Visit an authorized Apple seller/retailer.