ATHENS  In 2009, bankers for Goldman Sachs and Morgan Stanley pitched the Greek government on a plan to overhaul its money-losing railway system. Among the ideas was to lay off half of the system’s 7,000 workers and have the government take on roughly half of the company’s 8 billion euros in debt.

The suggestion did not fly. It was an election year in Greece, after all, and the country was already struggling to keep up the payments on its debt, which is higher in proportion to economic output than in any other nation in the European Union.

The plan was shelved, soon to be overshadowed by the country’s close brush with bankruptcy.

Losses at Hellenic Railways, however, continue to mount  at the rate of 3 million euros ($3.8 million) a day. Its total debt has increased to $13 billion, or about 5 percent of Greece’s gross domestic product.

Now, as a condition of Greece’s financial rescue, the International Monetary Fund is demanding that a solution be found. The fund and the European Union, which also chipped in to provide the bailout, are requiring that the debt of Hellenic Railways, as well as the off-balance-sheet obligations of other state-owned enterprises, be counted toward Greece’s official debt  which Greece has agreed to do.