ExThera claimed its device could cure cancer. But patients died.

The private jet took off from the Caribbean island of Antigua in April with three tanks of highly flammable compressed oxygen and a terminal cancer patient.

Kim Hudlow had chartered the plane for her husband, David. She crouched beside him during the five-hour journey to Florida, frantically adjusting the valve on one of the oxygen tanks as he struggled to breathe. A doctor had just told him that he was dying. She was terrified that he wouldn’t survive the theft.

It was a brutal turnaround. Six days earlier, Mrs. Hudlow and her husband, who had advanced esophageal cancer, had arrived on the tropical island full of hope that a new blood filtration treatment offered there would save Mr. Hudlow’s life – or at least would prolong it.

They were among about 20 families lured to Antigua by a California start-up called ExThera Medical and its secret billionaire partner, Alan Quasha.

ExThera, which has about 50 employees, makes just one product: a filter that it says can be used to remove tumor cells that circulate in patients’ blood and allow cancer to metastasize. Early last year, the company sold thousands of devices to Mr. Quasha’s private equity firm, Quadrant Management, which began using them on advanced cancer patients in a small clinic in Antigua.

Quadrant, which invests on behalf of Mr. Quasha and his family and has no outside investors, charged $45,000 for each treatment and advised patients to return to the clinic for regular sessions. He also urged them to refrain from chemotherapy between treatments.