Lawyers for Mr. Wang and Mr. Singh declined to comment. A lawyer for Ms. Ellison did not respond to a request for comment. A spokesman for the U.S. attorney’s office for the Southern District of New York, which is leading the criminal investigation into FTX, declined to comment.

A spokesman for Mr. Bankman-Fried declined to comment.

The government communications came at a relatively early phase of the investigation into Mr. Bankman-Fried, before Ms. Ellison and Mr. Wang pleaded guilty, and it’s possible that prosecutors’ understanding of some details of the case may have evolved.

But according to the documents, in 2020, one of the FTX software developers, known as CC-1, ran a query in a company database and learned that Alameda had a negative balance on the exchange of “approximately hundreds of millions of dollars.” The data led CC-1 to conclude that Alameda was “inappropriately using FTX.com customer funds,” according to the documents.

The executive raised the issue with Mr. Bankman-Fried, who responded that “it was okay,” the documents say, because the money Alameda had borrowed was backed by FTT, a cryptocurrency that FTX had invented.

Around the same time, FTX was undergoing an audit, according to the documents, and the high-level Alameda executive asked Mr. Bankman-Fried whether the auditors would raise any concerns about Alameda’s use of customer funds. “Bankman-Fried responded that auditors did not typically focus on such issues,” the documents show.

Concerns about Alameda intensified sometime around last September. The firm had recently lost about $5 billion, and Mr. Bankman-Fried discussed the possibility of shutting it down, according to the documents.

Around that time, the documents say, the software developer known as CC-1 told the other software developer, labeled CC-2, that Alameda had borrowed approximately $13 billion from FTX.

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