Having an individual account does not mean that money earmarked for you is sitting in a vault. E.g, our banking system gives everyone an individual account, but does not have enough cash to pay everyone back; and occasionally their other assets fall, resulting in them not being able to satisfy their obligations to account holders. This has happened often enough, that bank accounts are not required to be insured against it.

There has also been a common talking point of Congress stealing from social security to fund other expenses, which could also explain how it would not be able to pay even with individual accounts.