Bitfinex justified the decision by arguing that if the company was forced into liquidation, losses would have to be spread among all users.
"After much thought, analysis, and consultation, we have arrived at the conclusion that losses must be generalized across all accounts and assets," the company said in a statement on its website. "This is the closest approximation to what would happen in a liquidation context."
Bitfinex allows users to trade in several different digital currencies, including bitcoin, and deposit U.S. dollars in their account.
A total of 119,756 bitcoins, worth $70.5 million at today's price, were stolen as a result of a cybersecurity breach.
Bitfinex's decision is likely to disappoint many of the site's users who held assets other than bitcoins, warned Charles Hayter, chief executive and founder of digital currency comparison website CryptoCompare.
"What's disappointing is that the losses seem to be arbitrarily decided with larger operators being offered sweetners to keep them trading - and there is little clarity on BitFinex's company losses," Hayter told CNBC via email.
To compensate users, BitFinex is crediting each account with a digital token that will record how much the customer has lost as a result of the hack. These tokens will either be redeemed in full by the company in the future or they can be exchanged for shares in BitFinex's parent company, iFinex Inc. The statement did not specify any timeframe for the redemption.
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