On any given day, Pavlo Lazarenko looks like an ordinary stay-at-home dad, shuttling his three small children to school and waiting for his young wife to return home from work. Perhaps he’ll run an errand or two.

But Mr. Lazarenko, it turns out, is a world-class kleptocrat hiding in plain sight in suburban America. He is the former prime minister of Ukraine, where he was accused of siphoning hundreds of millions of dollars for his personal use. Transparency International named him one of the world’s 10 most corrupt officials.

He is wanted in his native Ukraine. He has been convicted of money laundering in the United States and, in absentia, in Switzerland. Moreover, his name recently surfaced in the leaked secret documents known as the Panama Papers in a long-running corruption case involving the alleged theft of Ukraine’s natural gas resources for himself and his political allies.

Even more, Mr. Lazarenko is waging two fierce battles with the United States government. One is over $250 million in offshore accounts in Guernsey, Switzerland, and elsewhere that the government claims are the fruits of Mr. Lazarenko’s “fraud, extortion, bribery, misappropriation and embezzlement.” The other is his effort to remain in the United States, where he has been seeking political asylum since arriving in 1999.