Upvote:2
Loss of Passport (§56(5) AufenthV) or Aufenthaltstitel §57a Pflichten der Inhaber von Dokumenten mit elektronischem Speicher- und Verarbeitungsmedium nach § 78 des Aufenthaltsgesetzes - AufenthV must be reported to the local Immigration office. Outside of Germany you must report the loss to a German mission, who will inform the responsible local Immigration office.
What happens then is not stated, but in the case of citizens of Türkiye it is known that the IO will authorise a visa to return to Germany.