The bankruptcy filing by American Airlines could saddle the obscure federal agency that insures company pensions with a $9 billion loss, officials say, raising the financial pressures on the debt-laden government fund and the possibility it could need a taxpayer bailout.

The Pension Benefit Guaranty Corp. is already facing a $26 billion deficit, the largest in its 37-year history, after being staggered by company failures across the country during the recession.

When companies fail, the PBGC picks up the obligation to pay out pensions to employees, and over the past fiscal year alone, the agency has assumed the responsibility for the pensions of 57,000 people.

If the agency is forced to take over the American Airlines pension plan, it would represent the largest-ever single claim on the PBGC fund. The largest previous claim came when the agency assumed the pension plans for United Airlines in 2005.

The financial pressures on the PBGC have provoked a debate over how to raise funds for the agency, which has never drawn from taxpayer dollars. Instead, the agency raises money from the companies whose pensions it insures through premiums.

“If the PBGC becomes responsible for the pension plans of American Airlines, the need for premiums to be raised will be greater,” said Joshua Gotbaum, the agency’s director. “The alternative is that at some point PBGC will be faced with the awful choice between needing a taxpayer bailout or not paying people pensions. We don’t want to get there.”

Whether American Airlines will terminate its pension plan and shift its obligations to the federal agency, however, has not been determined, the company said.

“A company’s Chapter 11 reorganization does not necessarily mean that a company’s pension plan will be taken over or terminated, although that is a possible outcome,” American Airlines spokesman Sean Collins said.

However, he added that one of the purposes of the bankruptcy is to enable the company to reduce its costs and that the company’s pension obligations make it harder for the airline to compete.

“American’s pension plans are very expensive — the company spends more on them than our competitors spend on their retirement plans,” he said. “Given American’s plans to reduce its costs to a more reasonable level in line with industry norms, these costs and many other factors are considerations when deciding whether to continue the pension plans.”

As American Airlines weighs dropping its pension plan, PBGC will be pushing the company to keep it. In recent years, the agency has helped persuade Delta and auto-parts maker Visteon to hold on to pension plans they might otherwise have dropped during reorganizations, Gotbaum said.

“When a company says we can’t afford the pension plan, we say we need to see the numbers,” he said. “They have to prove it.”

The growing financial pressures on the PBGC have stirred the debate over how to raise funds for the agency. Proposals to raise the fees, or premiums, that the PBGC charges companies have been languishing in Congress, in part because of business opposition to a price hike. Gotbaum has previously warned that without more such revenue, taxpayers may be forced to bail out the fund.

The pension plans offered by American Airlines, which cover almost 130,000 people, are obligated to pay $18.5 billion in benefits, according to the PBGC. But the company only has assets of $8.3 billion.

If the PBGC is forced to step in, retiree pension payments could be reduced slightly. The agency said it would be responsible for paying only about $17 billion of the total benefits, which would be disbursed over a long period.

“The PBGC is yet another government program that is facing a solvency crisis,” said David Kudla, chief executive and chief investment strategist of Mainstay Capital Management.

Based in Michigan, Kudla counts as clients hundreds of retirees from the auto-parts maker Delphi, which shifted its pension plan to the PBGC in 2009. He warned workers and retirees with pensions not to assume all of their pension will be there when they need it.

PBGC has $81 billion in assets and is obligated to pay out $107 billion in pension payments over time. The shortfall means the agency would eventually run out of money without additional funds.

“Many people who never thought this could happen to them or the company they worked for for decades are struggling to deal with the shortfall in the pension payments,” he said. “Every employee needs to recognize that the PBGC risk is real.”