Edra Denise Blixseth, age 55, is tiny, barely 5 feet 3, but she is at the center of a huge financial mess. According to personal bankruptcy papers her lawyer filed in March, she owes $500 million to $1 billion and has assets of barely half that, almost none of them liquid. Earlier this month, the court approved the sale of one of her most prized possessions - the private ski resort in Big Sky, Mont., known as the Yellowstone Club - to the private-equity firm of one of its members for $115 million. Just a year ago, that same buyer,...