The financial collapse of Braniff International, the latest of several large U.S. corporations to fail during the current recession, could strain the already burdened government agency that insures private pensions by adding $60 million to $70 million to its liabilities.

Braniff, which filed for protection under Chapter XI of the bankrupcty act while it attempts a financial reorganization, has fired most of its employes. A company spokesman could not say yesterday whether Braniff will terminate its pension plan--an action that would add nearly $70 million to the liabilities of the Pension Benefit Guaranty Corp.

The PBGC, set up by Congress in 1974, is already running a deficit of $190 million, its documents indicate. That is, if it had to meet all its liabilities at once instead of over a period of years, it would fall short by that amount. However, that does not mean that the PBGC is in danger of running out of money any time soon to pay retirees' benefits. It has sufficient cash now. In the last fiscal year, it had income of $86.7 million in premiums and paid $61.1 million in benefits.

The current insurance premium paid by single employer plans is $2.60 annually per worker covered. If there were no increase in premiums, PBGC officials estimate that the agency could go on paying benefits for another five to 10 years or longer without going broke, although its deficit would increase.

"It would be ironic if the agency that is trying to protect employes' benefits were to be badly funded itself," said Deene Goodlaw Solomon, acting chairwoman of the PBGC's advisory committee.

The PBGC is about to ask Congress to raise the single employer premium to $6. By so doing, the agency hopes to eliminate its deficit in five years.

Should Braniff terminate its plan, it would mean an additional 67 cents to $1 would have to be added to the $6 premium request.

Despite scattered opposition to the big hike from some corporations and members of Congress, it is expected to pass.

However, the PBGC's calculations of a $6 premium were made earlier this year before the bankruptcies of Braniff and other large corporations. It is possible that these and other anticipated failures may increase the PBGC's burden and hence the premium. The PBGC has calculated that the failure of just two large companies--Chrysler Corp. and International Harvester Co.--could require a $20 premium to cover their $2 billion in unfunded liabilities.

"I am worried because the system should be able to absorb a significant size termination now and then. But I would hate to see several bankruptcies in close proximity," said Robert E. Nagle, who headed the PBGC for two and a half years until his resignation six days ago.

Officials of Wickes Corp., a $4 billion retailer, and AM International Inc., which filed for Chapter XI reorganization last month, said yesterday that they did not intend to terminate their pension plans.

The PBGC estimates that the demise of Braniff's five pension plans, covering 10,000 employes, demise would increase its potential liability by $60 million to $70 million. Alicia H. Munnell, vice president of the Federal Reserve Bank of Boston, finds a potential liability of $115.6 million by using different interest rate assumptions.

In a recent article in the New England Economic Review, Munnell declared that the PBGC "is in a potentially vulnerable position." She considers a $20 premium the breaking point at which many companies would leave the insurance program.

The agency insures against plan terminations. The number of pension plans abandoned by companies rose by 26 percent last year. Very few terminating plans in the past lacked funds to pay guaranteed benefits. But the increasing rate of business bankruptcies--up 45 percent in 1981--makes it likely more will be underfunded.

In such cases, the PBGC can lay claim to the plan's assets plus 30 percent of the market net worth of a company to satisfy the lack of funding. Munnell makes the argument that it is perfectly legal--and, indeed, in their financial interest--for companies with unfunded benefits in excess of 30 percent of net worth to terminate their plans, transfer their liability to the PBGC and set up Individual Retirement Accounts for their employes. On Munnell's list of 22 are Chrysler, Braniff, International Harvester and Pan American.

Should that happen, the burden might become too large for the PBGC. The agency has a $100 million line of credit on the U.S. Treasury, but Nagle says it could only be used to pay benefits, not reduce its deficits. Eventually the PBGC could find itself in the same situation as the Social Security system.