The former chairman of Wyckoff Heights Medical Center in Brooklyn, who stepped down five months ago, is on life support after being injured there, several doctors associated with the hospital said Tuesday. The former chairman, Emil J. Rucigay, a lawyer, was pressured to resign by doctors who said he had been an overly passive leader after the Brooklyn district attorney began investigating allegations of cronyism and insider dealing by management at the hospital. The hospital’s newly appointed chief executive said the hospital was investigating Mr. Rucigay’s care and would report the case to the State Health Department.