Prudential would appear to be the first partner company of Wells Fargo to get caught in the aftermath of the bank’s admission three months ago that thousands of its employees had opened unauthorized accounts in bank customers’ names. The bank has fired more than 5,000 employees and paid fines of $185 million in connection with the scandal.

Wells Fargo employees were encouraged to aggressively sell a mix of products to their customers, former Wells Fargo employees said, including insurance offerings from partners. The renters’ insurance Wells Fargo sold for Assurant had some similarities to Prudential’s MyTerm policies: Both were fairly inexpensive products that could be bought in a few minutes, after the applicant filled out a brief online questionnaire.

“As we have consistently reinforced, if we identify any instances where a customer received a product they didn’t ask for, we will make it right,” Mr. Folk said. The bank eliminated its sales goals for retail bankers in October, he noted. It no longer offers incentives for selling customers additional products, including insurance policies.

Also on Monday, Alex Perea, a Wells Fargo customer who said he had been victimized by the insurance scheme, filed a lawsuit against Prudential. He and his lawyers are seeking class-action status for the case.

Mr. Perea, of Arizona, received a collections notice in October about unpaid premiums on a MyTerm policy, according to his complaint. A Wells Fargo customer since 2010, Mr. Perea “never authorized anyone to seek life insurance on his behalf” and was unaware that a Prudential policy had been taken out in his name, he said in the lawsuit.