From time to time over the years, Congress has enlisted private enterprise to try to solve certain social or economic problems. It has created special kinds of companies, with special links to the government but owned by private investors who put up the money, to reap the benefits of success and pay the price of failure.

These companies, known as government-sponsored enterprises (GSEs), have generally provided excellent investment returns for their private investor-owners as they have helped pump lower-cost funds into such diverse markets as home buying, agriculture and education.

But now, for the first time, the government and GSE shareholders face these big questions: What becomes of one of these companies if the problem it was meant to solve goes away or if the government's approach to it changes so fundamentally that the enterprise is no longer needed? Further, is there a way to extricate the government from the company that is both fair to the government and fair to the company's shareholders?

Holders of Student Loan Marketing Association (Sallie Mae) stock are about to find out.

They already have taken a hair-curling beating. Since 1993, when the Clinton administration first indicated it intended to have the government take over the student loan market -- the company's main business -- Sallie Mae's stock has plunged by roughly half, from a high of about $76 in September 1992. The nose dive has cost stockholders $4.4 billion.

"This enormous evaporation of the shareholders' money exceeds by nearly 50 percent all of the earnings that Sallie Mae has reported over the course of its 21-year existence," said Robert E. Torray, who heads Robert E. Torray & Co., an investment management firm in Bethesda that holds about 1.5 million Sallie Mae shares.

Sallie Mae's management, perhaps making virtue of necessity, has embraced privatization. It has opened negotiations with the Treasury and Education departments to surrender its congressional charter so that it can seek new and profitable lines of business.

Sallie Mae chief executive Lawrence A. Hough said there is a range of endeavors that the company could successfully undertake, given its expertise and relationships. Not only could it service loans to students and others, it also could offer educational institutions a way of contracting out many of their financial and student aid operations, he said.

Other areas where highly efficient data-processing is important, such as health care, also offer opportunities, Hough said.

However, the strategy has not made all the stockholders happy. A dissident group led by former Sallie Mae executives has launched a proxy fight to elect to the company's board an eight-member slate pledged to adopt different tactics.

Although they say they are "philosophically committed to privatization . . . we believe the company is not ready yet" for it, said Paul Carey, a business partner of Albert L. Lord, a leader of the dissident group.

The dissidents note that Sallie Mae stock has bounced back to $47.50 recently from $35.37 1/2 on April 10. It closed Friday at $46.

The dissidents complain that the management approach is hasty, will fail to achieve the best value, and doesn't consider shareholder interests enough. The battle comes to a head Thursday at the annual shareholder meeting here.

Whatever the outcome, however, the fundamental questions surrounding the endgame of a government-sponsored enterprise are far from answered. Different political winds are blowing on Capitol Hill from a year ago, and what the government ultimately will need or demand from Sallie Mae remains unclear.

A House committee is at work on a bill that would set the terms for Sallie Mae's privatization, and may vote on it as early as this week.

The Clinton administration wants the company to pay an "exit fee" meant "to recognize the benefits Sallie Mae has received because of its GSE status."

The amount or form of this fee is not yet determined. But Deputy Assistant Treasury Secretary Darcy Bradbury told a House hearing earlier this month the company could be required to issue warrants the government could later convert into stock if the privatized company is successful. This "would enable the United States to participate in the success of" the privatized company, she said.

At the same time, the Education Department, despite its professed confidence in direct government lending to students, is plainly worried that something might go wrong. It would like to be sure students would still be able to get loans.

In the past, Sallie Mae has been the lender of last resort, and the department wants to make sure it would continue to be available in an emergency, according to Education officials.

In fact, that is what Sallie Mae was created to do -- and has done.

When Congress chartered Sallie Mae in 1972, its mission was to create a secondary market in government-guaranteed student loans. The government was anxious to make these loans widely available. Banks and other lenders were more willing to make the loans if they knew there was a ready market in case they decided to get the loans off their books.

By most accounts, Sallie Mae carried out its mission admirably. And, as the exploding cost of education drove up the need for student loans, the company and its shareholders have ridden that wave to handsome profits.

But even as its profits ballooned, problems dogged the government's guaranteed student loan program. Default rates soared, particularly among students at some for-profit trade schools, costing the government billions. At the same time, the increases in tuition and other costs at colleges provoked complaints from middle-class parents.

Sallie Mae stuck to its knitting, concentrating on running its operations as efficiently as possible and letting the government worry about policy questions.

In early 1993, Sallie Mae officials awoke to find the president of the United States describing their company as part of the problem, not part of the solution. Clinton accused lenders and others of making risk-free profits, and called Sallie Mae "the biggest middleman in the whole thing."

Making good on his word, Clinton pressed Congress to allow the government to take over student lending itself. If that were done, or so the theory went, interest payments would go to make new loans instead of to the banks, Sallie Mae and other players in the system, and student loans would be cheaper.

Congress agreed, at least partially. It enacted a law that would have the government take over as much as 60 percent of the student loan market by the 1998-99 academic year. That takeover has begun.

Sallie Mae's Hough insists the company will remain committed to student lending, and will work with the government on new programs, if needed. "It's our business, we have decades of experience," he said.

But he warned the House hearing that if Congress or the administration insists on exit terms that the company's stockholders consider unfair, the stockholders will reject them. The company will not agree, for example, if the exit fee is too high, if the company is forced to make up for the revenue that would be lost from privatization or if there are serious restrictions on the businesses it can get into. Since last year, Sallie Mae has been required to pay the government an "offset fee" of three-tenths of 1 percent on all the loans it purchases -- a total of $251 million over five years.

"At the end of the day, our shareholders are going to vote up or down," Hough said. "Up, we are on our way. Down, we are back to the drawing boards and confronting some truly difficult alternatives to try and make this thing work." * CAPTION: SALLIE MAE'S TUMBLE (This chart was not available)