Still, accounting experts say the shadow financial system needs some sunlight.

“How can anyone — regulators, investors or anyone — understand what’s in these financial statements if they have to dig 15 layers deep to find these kinds of interlocking relationships and these kinds of transactions?” said Francine McKenna, an accounting consultant who has examined the financial crisis on her blog, re: The Auditors. “Everybody’s talking about preventing the next crisis, but they can’t prevent the next crisis if they don’t understand all these incestuous relationships.”

The story of Lehman and Hudson Castle begins in 2001, when the housing bubble was just starting to inflate. That year, Lehman spent $7 million to buy into a small financial company, IBEX Capital Markets, which later became Hudson Castle.

From the start, Hudson Castle lived in Lehman’s shadow. According to a 2001 memorandum given to The New York Times, as well as interviews with seven former employees at Lehman and Hudson Castle, Lehman exerted an unusual level of control over the firm. Lehman, the memorandum said, would serve “as the internal and external ‘gatekeeper’ for all business activities conducted by the firm.”

Image Lehman Brothers’ headquarters in Midtown Manhattan in 2008. It is now the offices of Barclays Capital. Credit... Patrick Andrade for The New York Times

The deal was proposed by Kyle Miller, who worked at Lehman. In the memorandum, Mr. Miller wrote that Lehman’s investment in Hudson Castle would give the bank and its clients access to financing while preventing “headline risk” if any of its deals went south. It would also reduce Lehman’s “moral obligation” to support its off-balance sheet vehicles, he wrote. The arrangement would maximize Lehman’s control over Hudson Castle “without jeopardizing the off-balance sheet accounting treatment.”

Mr. Miller became president of Hudson Castle and brought several Lehman employees with him. Through a Hudson Castle spokesman, Mr. Miller declined a request for an interview.

The spokesman did not dispute the 2001 memorandum but said the relationship with Lehman had evolved. After 2004, “all funding decisions at Hudson Castle were solely made by the management team and neither the board of directors nor Lehman Brothers participated in or influenced those decisions in any way,” he said, adding that Lehman was only a tenth of Hudson’s revenue.