Lehman Brothers Holdings Inc.'s historicbankruptcy burned the once-highflying securities firm's investors, employees and many others. But five years later, a group of hedge funds has found a way to profit handsomely from it.

In the past 18 months, billions of dollars in distributions from the Lehman bankruptcyestate have been paid to investors--including Elliott Management LP and Paulson & Co.--who snapped up claims in the years following the firm's collapse, according to company documents, court filings and people familiar with the matter.

Paulson, which made a fortune on a well-timed housing-market bet in the early stages of the financial crisis, is up more than $1 billion on its investments in Lehman claims, while Elliott is ahead by more than $700 million, according to the people familiar with the matter.

After Lehman failed in September 2008, some creditors didn't want to wait for their money, or take a chance that they wouldn't get paid at all. Some distressed-investing hedge-fund managers were willing buyers of their claims, deploying teams to study Lehman's balance sheet to identify potentially valuable assets they could buy at discounts.

For many of them, the strategy worked. Since early 2012, when Lehman's payback plan became effective, nearly $50 billion has gone back to creditors. Total payouts--which come as assets Lehman held when it failed are liquidated--are expected to hit about $80 billion as the bank recovers more cash through settlements with its foreign affiliates and derivatives counterparties, according to regulatory filings and court documents.

'The majority of the money is moving from Lehman's offices to people that are on these 20 blocks,' said C.J. Lanktree, an executive vice president at distressed-investment firm Solus Alternative Asset Management, one of the firms that has profited from Lehman claims. He was speaking from Solus's office in midtown Manhattan, located near other hedge funds, including Elliott and Paulson.

Elliott--already a creditor of Lehman's when it filed for Chapter 11 protection, as one of the bank's prime-brokerage customers--bought Lehman claims with a face value of $587 million in one two-month period in 2011, according to regulatory filings.

The firm, with roughly $21 billion of assets under management, owns debt on many of the rungs of Lehman's capital structure, according to people familiar with the matter. One of these people said the employees in charge of monitoring Lehman wire-account deposits watch them 'like a hawk' to ensure there are no discrepancies in Elliott's recoveries.

Paulson, a longtime holder of Lehman unsecured bonds, has been buying other Lehman claims over the past two years, according to people familiar with the firm's investments. The firm, which helped lead the settlement negotiations that led to Lehman's creditor-payment plan, has more than $4 billion invested in Lehman claims, these people say. Other investment firms, including Halcyon Asset Management LLC and King Street Capital Management LP, have also made money on Lehman claims, people familiar with the matter say.

That outcome was far from assured five years ago. Creditors including Google Inc., International Business Machines Corp., the Massachusetts Bay Transportation Authority and the New York Giants football team asserted more than $1.3 trillion in claims after Lehman filed for bankruptcy, an event that triggered a sharp downdraft in financial markets whose effect on the global economy lingers to this day. While some original creditors held on to their claims, thousands of others sold, court filings show.

'In the beginning, you don't know what the distributionschedule is like,' Mr. Lanktree of Solus said. 'You're taking a lot more risk' by holding, or buying, a claim, he said. As the years ticked by, Lehman and its creditors sorted through claims and negotiated settlements to establish a pecking order for repayment. Along the way, uncertainty began to give way to optimism for investors.

For Solus, the critical moment came after a 2011 meeting with about 20 other big Lehman creditors, where a plan to distribute tens of billions of dollars in Lehman assets was finalized. Creditors of various Lehman subsidiaries would get more than those holding unsecured claims against the parent company.

For instance, some claims against derivatives unit Lehman Brothers Specialty Finance that Solus bought for around 20 cents on the dollar now are worth more than 55 cents on the dollar, according to several people who own them. Lehman-related holdings in one Solus fund have gained 40%, according to a person familiar with the matter.

Still, investing in a bankruptcyunprecedented in its size and complexity has presented a unique set of challenges. At Solus, it was tough to keep the Lehman checks straight as they started coming in, people at the firm say. Dozens were mailed to Solus's office, while at least six others went to a custodian for the firm in Houston. Solus ultimately arranged to get its money through wire transfers, the firm said.

Solus has three portfolio managers, a legal expert and an analyst who 'spend a ton of time' dealing with the Lehman investments, Mr. Lanktree said.