For a bank, a federal indictment is the ultimate black mark.

That’s why lawyers who deal in securities law say the world’s largest banks will agree to almost anything to avoid getting hit with an indictment connected to the developing scandal over the alleged manipulation of a key bank rate—the London interbank-offered rate (LIBOR).

Although the US Department of Justice is not commenting, some news reports have said it might target a bank, not just the employees responsible for the alleged transgression. The reason to go after both: frustration by officials that a financial institution was a repeat offender or perhaps impeded an investigation.

“Maybe in the mind of the prosecutor, there is such an institution and the prosecutor says, ‘We proceeded civilly with cases against you, and there is no recognition that something culturally has to change with you guys,’ ” says Jim Keneally, a partner in the white-collar practice at Kelley Drye & Warren, a New York law firm. “Maybe you need to punch them in the nose or issue a shot across the bow.”

Prosecutors have been poring over documents related to the actions for two years. What they seem to have discovered is that in the wake of the 2008 financial-industry collapse, employees at large banks were underreporting the interest rates their banks were paying to borrow money from other banks.

This partly bolstered the banks’ profits and made the banks seem to be better credit risks. However, it also hurt pensions and other institutions, which were using the LIBOR rate to offset risks in their own portfolio. Some of those institutions are now suing the banks.

Several state attorneys general are also investigating the actions. In the past, the AGs have sometimes worked together to get settlements, such as the 1998 agreement by the major tobacco companies to pay the states $206 billion over 25 years.

Documents released by the New York Federal Reserve show that US regulators were concerned about irregularities with the LIBOR rate setting. US Treasury chief Timothy Geithner, then head of the New York Fed, wrote to British regulators urging them to take action to correct the situation. Apparently little was done.

The LIBOR rate is determined when banks call the British Bankers’ Association to report what they paid to borrow large sums of money, ranging from overnight to one year. The rate is set at 11 a.m. each weekday and published by Thomson Reuters.

If the banks reporting their lending rates have been giving intentionally inaccurate numbers, that could be a crime, says Robert Mintz, a former prosecutor who is now a partner at McCarter & English in Newark, N.J.

“If you issue false statements and you know someone is relying on them, that is enough for criminal liability,” he says.

Mr. Keneally says the banks could be charged with “fraud.”

Normally, in the case of a bank, a shot across the bow is usually enough to get the board of directors busy. That’s what apparently happened at Barclays, which agreed to pay a $450 million fine and allow its chief executive, Robert Diamond, and other top executives to resign.

An indictment would be the equivalent of a knockout.

“Basically no bank can survive a conviction,” says Annemarie McAvoy, an adjunct professor at Fordham Law School who was formerly in the legal department at Citibank. “Banking is based on trust, and if the customers lose faith, they can move to another bank.”

Ms. McAvoy thinks federal prosecutors are using the threat of prosecution as a bargaining chip. She expects banks will agree to fines, outside monitors, and the tightening up of their compliance programs.

“The government has a big stick it can use,” she says.

How big that stick can be was apparent in 2002, when the government indicted the accounting firm Arthur Andersen in the wake of the Enron collapse. Andersen had been Enron’s accountant and did not catch the fraud perpetrated by the company and its executives. After the indictment, Andersen collapsed.

Three years later, the US Supreme Court ruled that the Department of Justice had overreached, and it threw out the case. But it was too late for the firm.

“Arthur Andersen was a miscalculation by the government,” Mr. Mintz says. “They threatened to indict but expected the partnership to work out some resolution that would have prevented that from occurring. But that did not happen.”

In the wake of Andersen, he thinks prosecutors have become more warier, since an indictment can harm innocent people. “If it’s a publicly held company, innocent shareholders can be hurt,” he says. “Even if it’s not a publicly held company, innocent employees could be harmed, which is why they usually focus on individuals.”

That may be one reason that now, prosecutors might opt for a “deferred prosecution agreement,” which would give a bank time to put in new systems to prevent future abuse. “The implication is if you don’t do something to prevent future abuse, you can be hit with criminal charges,” says McAvoy. “Banks are so petrified of criminal prosecution.”