Taxpayers will soon shed their last holdings in the American International Group, more than four years after a rescue by the federal government during the most chaotic days of the financial crisis.

The Treasury Department said Monday that it planned to sell all of its remaining 234.2 million shares, or 15.9 percent of the company, in a public offering. At current prices, that would raise more than $7.8 billion.

The stock sale, if completed, would realize a goal few dreamed possible in September 2008. As Lehman Bros. filed for bankruptcy, government officials scrambled to rescue AIG, which had become deeply intertwined with many Wall Street and European banks through its underwriting of credit-default swaps. The fear was that a collapse of the insurance giant could bring down the global financial system.

In the crisis, the government ended up extending lifelines to a number of financial institutions and to companies like General Motors. But it was the bailout of AIG that resonated most deeply among the American public as a symbol of risk-taking and excess on Wall Street – and Washington’s complicity in it. At one point, the government had made more than $182 billion available to support AIG. Billions of that went to pay claims that the banks had on the insurer.

Public anger over the bailout prompted congressional hearings, litigation, protests and widespread criticism from both the political left and the right.

Even Ben S. Bernanke, the Federal Reserve’s chairman and one of the architects of the bailout, has said that the necessity of the plan made him angry.

“We had no choice but to try to stabilize the system because of the implications that the failure would have had for the broad economic system,” he told a Senate panel in 2009.

At the time, critics feared that the company would be forced into a fire sale of assets to repay those loans, a sale that would deeply shortchange taxpayers.

Instead, the federal government has said that it expects to walk away from AIG with a profit – about $15.1 billion to date, by the Treasury Department’s reckoning. That has followed both a steady stream of stock sales over the last two years and a resurgence in the insurer’s core operations.

“It’s gone way better than anyone expected in 2008 and 2009,” said Linus Wilson, an assistant professor of finance at the University of Louisiana at Lafayette. “People thought we’d put money down a dry hole and would never see it again.”