In 2014, the Chinese city of Haimen on the mouth of the Yangtze River set out to build a large apartment complex and turned to Bank of Nanjing Co. for about $29 million in financing.

The bank was happy to oblige but it didn’t call the money a loan, according to people familiar with the matter. It was added to Bank of Nanjing’s balance sheet as an “investment receivable,” a loosely regulated category of assets that allows bank officials to set aside little or nothing for potential losses.

Bank...