I am a US citizen and permanent resident of Germany. I am in the process of becoming a German citizen. This requires me to renounce my US citizenship, but the US Consulate in Germany is extremely backed up. I have heard of people travelling to renounce citizenship, but my understanding is that I would give up my passport during the appointment. Since I have no other citizenship, I would then have to return to Germany with no passport at all. All I would have is my German residence permit (along with various paperwork that would explain my situation). Is it possible to travel this way?
Germany requires a valid passport for entry into the territory, as laid out per AufenthG § 3, a residence permit alone is not valid for entry.
(1) Foreigners may enter or stay in the federal territory only if they possess a recognised and valid passport or passport substitute, unless they are exempt from the passport requirement by virtue of a statutory instrument. For the purpose of residence in the federal territory, possession of a substitute identity document also suffices in order to meet the passport requirement (section 48 (2)).
Once you renounce your US citizenship, you will be considered (for the German authorities at least) to be stateless and will no longer have a US passport to travel with.
This normally must be done outside the US, so I assume you wish to do this from within the Schengen Area to avoid any regular passport control.
The German Einbürgerungszusicherung will probably be required by the US officials (outside of Germany it may have to be translated).
This, togeather with a letter confirming that your passport has been retained would explain the reason why you are returning to Germany without a required travel document. Because of this, if you are actualy found out, it would probably have no further consequences.
This letter would also be usefull when applying for a stateless passport (see below).
Part of the process is that a Certificate of Loss of Nationality will be issued immediately, but will first be sent to the State Department for 'review' and later sent back to you.
Even before FATCA this could have taken quite some time (early 1980's 6 months).
The confirmed Certificate of Loss of Nationality is what the German authorities require to complete the naturalization process.
During this time you are eligible for a stateless passport that will be issued by the local immigration office (see link for Berlin below).
With this travel document, togeather with your residence permit card, you can travel to other countries.