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Customers of Mt. Gox, once the world’s largest Bitcoin exchange, are closer to getting back at least some of the money they lost this year when it shut down and announced that their funds had gone missing.

The bankruptcy trustee for Mt. Gox, which is based in Tokyo, announced on Wednesday that it would work with a California-based Bitcoin exchange, Kraken, to return the money left in the estate to the company’s 127,000 creditors.

Jesse Powell, Kraken’s chief executive, said during a news conference in Tokyo on Wednesday that his company would help with the claims process, including evaluating the assets owed to creditors, and that it would assist in the investigation of Mt. Gox’s collapse. He said the trustee would have the final decision on payments in Bitcoin.

“Allowing the creditors to go on without reinvestment, I think, would be very wrong,” he said, adding, “We’ve got to have the money that was locked up for the last 10 months returned as soon as possible.”

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On the question of whether Mt. Gox would be revived, Mr. Powell said: “There are no assets, no brand. There is nothing to speak of to revive.”

The decision is a somewhat unexpected development in the saga of Mt. Gox’s collapse, which rocked the upstart world of Bitcoin.

When Mt. Gox initially went down in February, the company’s chief executive, Mark Karpeles, said the company had either lost or been robbed of 850,000 coins, worth about $500 million at the time. Mr. Karpeles said that 100,000 of the missing coins belonged to the exchange but that the rest were owned by customers.

A few weeks after Mt. Gox shut down, Mr. Karpeles announced he had found about 200,000 coins that he had thought were missing, leaving 650,000 still unaccounted for.

Mr. Karpeles has said that hackers appeared to have stolen the money. Yet while several law enforcement authorities in Japan and the United States have reportedly been investigating, they have produced few answers. As part of its mandate from the bankruptcy trustee, Kraken will participate in the investigation.

The price of a Bitcoin has dropped by half since Mt. Gox closed but has recently stabilized at just under $400.

The 200,000 coins discovered after the exchange shut down appear to represent the bulk of the estate’s assets, though the trustee has not recently commented on his success in recovering missing assets. In a July filing, the company said that in addition to 202,100 coins, it had 779 million yen, or about $6.6 million, in other assets.

The court-appointed trustee previously suggested that the remaining coins could be converted into dollars before being returned. But many creditors resisted, worried that the conversion of all that Bitcoin into dollars would depress the digital currency’s value.

Several companies in the virtual-currency industry vied to take over either the business or assets of Mt. Gox, or both, an attractive proposition given the size of its customer base. A group called Sunlot Holdings, led by John Betts, a former Wall Street executive, said in March that it had signed an agreement with Mr. Karpeles to revive the exchange. But that deal quickly fell apart.

The choice of Kraken is notable because it is not one of the largest Bitcoin exchanges. The company has catered primarily to European customers, through a partnership with a German bank, and recently opened in Japan. But Kraken has developed a reputation for taking a careful approach that has kept it in good standing with regulators.

The job of reimbursing Mt. Gox creditors should be a boon for Kraken because they will most likely be required to open an account with Kraken to get their money back. That should lead to a significant increase in the number of people with Kraken accounts, and some of them could continue using the exchange.

Hisako Ueno contributed reporting from Tokyo.