Pritzker has spent a good bit of her career fending off criticism about her family and her role in its businesses. U.S. government officials sued the Pritzkers to collect taxes from her grandfather Abram's estate after he died in 1986.

The case centered on hundreds of trust funds Abram had set up in the Caribbean to avoid taxes. In 2001, an Illinois savings and loan that was once headed by Penny collapsed. Some 1,400 depositors are still out about $10 million, says Clinton Krislov, an attorney suing Penny and bank officers on their behalf. That same year, part of her family turned on her when seven brothers and cousins alleged in court documents that she'd enriched herself at their expense.