KIEV, Ukraine — When the Ukrainian prosecutor Kostiantyn H. Kulyk compiled a seven-page dossier in English that accused the son of former Vice President Joseph R. Biden Jr. of corruption, he helped set off a political firestorm that has led to the impeachment investigation of President Trump.

But even as he was reopening a corruption case related to Hunter Biden’s service on the board of Burisma Holdings, a major Ukrainian gas company, Mr. Kulyk himself was under a cloud of suspicion.

He has been indicted three times on corruption charges and accused of bringing politically motivated criminal cases against his opponents. In a Ukrainian security clearance form, Mr. Kulyk admitted having ties to a warlord in eastern Ukraine accused of working for the Russian intelligence services.

Yet none of this — including the case related to the Bidens — has seemed to harm the career of Mr. Kulyk, who remains a department head in the Ukrainian prosecutor general’s office under a new president, Volodymyr Zelensky.