Monty Bennett’s lodging business has been hit hard by the pandemic. He said Ashford Inc. and its subsidiaries have laid off or furloughed 95% of their 7,000 employees. An affiliated company, the owner of 117 hotels, stopped making payments on most of its $4 billion in debt, he said.

But during the crisis, Mr. Bennett and other preferred shareholders still got paid millions of dollars in preferred dividends. At one of the companies, Ashford Hospitality Trust, payments to third-party preferred shareholders were declared by its...