Francis deSouza, the chief executive of the biotechnology giant Illumina, didn’t know what he was in for when he resisted Carl Icahn’s demand in March for three seats on the company’s board.Mr. Icahn, the billionaire investor, hired a private investigator to dig up dirt on Mr. deSouza. He wrote letters to Illumina shareholders lambasting Mr. deSouza’s leadership and publicized details of his divorce. By June, Mr. deSouza and the chairman of Illumina had resigned. One of Mr. Icahn’s allies joined the board.Such bare-knuckle tactics have made Mr. Icahn the nightmare of many a chief executive and changed the fate of some of America’s most iconic companies, including Apple, RJR Nabisco, Blockbuster and Netflix.But in May, Mr. Icahn, 87, found out what it’s l …
