I've never heard that specific claim before, but what immediately came to mind was the MEFO Bills used to fund rearmament in the 1930s, as while not a Ponzi scheme, it was certainly dishonest economics, so if I had to guess, that is what is being referred to. For more information on it, I would recommend this answer from /u/kieslowskifan, or this one from /u/parksungjun. Hope that helps!

To clarify the question, the version I've heard is that the Nazis spent unsustainably and relied on wealth stolen from invaded countries to maintain the economy -- a sort of "Ponzi scheme." Is this true?

I would describe the MEFO bills mentioned below as more of an accounting gimmick to circumvent restrictions in the Treaty of Versailles. Remember, the treaty specified reparations to be paid and restricted the sorts of military equipment Germany could purchase. As such, the allies had an interest in both Germany's financial condition (including debts), and preventing the production of heavy military equipment like tanks, warplanes, and battleships.

Germany wanted all this military equipment and had to pay for it somehow, so it created a fake company, Metallurgische Forschungsgesellschaft (MeFo), to issue debts to the armaments manufacturers. Enron did something similar, borrowing in the name of subsidiary firms so investors did not realize that the company was insolvent.

There are a number of ways the German economy of the thirties and forties was a Ponzi scheme. The rearmament stimulated the economy, and the Germans then used the weapons to take resources like precious metals, raw materials, and slave labor from other countries. There were also forced saving programs for the German workers, so they were forced to loan money to the government and unable to access their wages. The pre-war economy also used dumping to accumulate enough foreign currency to afford needed war materials from other countries, like steel from Sweden.

The best book on this topic is Wages of Destruction by Adam Tooze