DETROIT — The U.S. government expects to sell the last of its stake in General Motors by the end of the year, bringing an end to a sad chapter in the company’s storied history.

The Treasury Department today said it still owns 31.1 million shares of the auto giant, less than 2 percent. It plans to sell the shares by Dec. 31, as long as the price holds up.

The government received 912 million shares in exchange for a $49.5 billion bailout during the financial crisis in 2008 and 2009. So far it has recovered $38.4 billion of the money, but selling the remaining shares at Wednesday’s $37.69 closing price gets the government $1.17 billion, leaving taxpayers short by roughly $10 billion.

The government says the bailout was needed five years ago to save the American auto industry and more than a million jobs. It never expected to get all of the money back.

“Had we not acted to support the automotive industry, the cost to the country would have been substantial — in terms of lost jobs, lost tax revenue, reduced economic production and other consequences,” Deputy Assistant Treasury Secretary Tim Bowler said in the statement.

Taxpayers’ initially got a 61 percent stake in GM in exchange for the bailout. Treasury gradually has sold off its stake since a November 2010 initial public offering.