Maurice R. "Hank" Greenberg built American International Group Inc. into a global financial-services powerhouse during nearly 40 years at its helm. But as the firm in 2008 neared collapse, three years after his departure, he couldn't get calls, emails or faxes returned as he tried to offer his help, people familiar with the matter said.

Now, the 89-year-old Mr. Greenberg is getting his chance at revenge—and, as he sees it, justice—by challenging the government's historic bailout of AIG.

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