A pressurisation issue at 35000 feet is a killer item. You make a screaming descent to 10000, tell ATC if you have the bandwidth, and then sort it out. You might need to buy some Jet fuel or take a commercial flight from somewhere but you and your family is alive. My guess: "They will find out that the masks for the passengers came down and the pilot left his seat during AP set to 36000 feet to look after his passengers. Then he passed out too and the plane flew on AP until out of fuel."