This is true

The issue:

In 1965 a man from Australia, who weighed 456 pounds, actually survived without eating for 382 days, living entirely off his body fat and supplemental vitamins.

Yes, Snopes says. It bases its conclusion on a March 1973 case report in the Postgraduate Medical Journal, as well as other scientific reports. His weight decreased from 456 to 180 lb. Five years after undertaking the fast, his weight remains around 196 lb.

The patient began his fasting in the hospital, but he completed most of his fast at home, testing his blood glucose and urine regularly. In response to the results of those tests, the doctors occasionally added other non-caloric supplements to his vitamin regime, including potassium supplements and sodium supplements, to correct for deficiencies.