Every person with residence in Germany has to be registered there (general compulsory registration). This includes the obligation to register change of residence within a week after the move to the registration office in Germany. Not doing so constitutes a misdemeanour and carries an automatic financial penalty.
If you leave your place of residence in Germany and move abroad, you need to deregister with the relevant registration office in Germany. Abroad you might need the deregistration certificate for example to present it to the German mission abroad when dealing with passport issues such as changing the place of residence in your passport or at the issuing of new passports.
If you are still registered in Germany, you need to apply with the relevant authority in Germany if you want to be issued with a new travel passport. The German mission abroad is in this case not responsible and can only help you in exceptional circumstances. In addition, there will be additional fees for the passport as well as a delay in the processing, since the German mission in such cases first has to receive authorization from the local German authority responsible for issuing the passport.
Detailed information on German Registration Law is available here: