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Fabrizio Costantini for The New York Times The abandoned train station in Detroit, which is bankrupt.

Detroit had a bit of rare good fortune as it hurtled toward bankruptcy last summer — a couple of banks were willing to let it out of some expensive financial contracts, called interest-rate swaps, without paying in full the usual steep termination fees.

But since then, an insurance company has been seeking to block the deal, lining up allies among Detroit’s other creditors. The insurer, Syncora Guarantee, contends that Detroit’s good deal was struck at its expense, improperly stripping it of cash that Detroit now wants to use to tide itself over as it goes through the biggest Chapter 9 municipal bankruptcy case in American history.

Syncora says the city already pledged the money to it as collateral on a complex borrowing package that Syncora insured. It wants the judge in the case to block Detroit’s settlement with the other participants in the swap transaction, UBS and Merrill Lynch — the only out-of-court settlement the city managed to reach with its creditors before filing for bankruptcy on July 18.

Syncora’s objections have been receiving support from some of Detroit’s other bond insurers and investors that bought the securities that Syncora insured. A hearing on the evidence that was scheduled to begin on Tuesday in federal bankruptcy court was postponed Monday afternoon after the city’s emergency manager, Kevyn Orr, said it would be worthwhile to continue seeking an out-of-court solution in mediation. Judge Steven W. Rhodes, who is handling the case, has strongly urged Detroit’s thousands of creditors, including Syncora, to try to settle out of court lest the case drag on forever, destroying any hope of recovery.

The court battle also shows the difficulty of following through with the complex municipal borrowing deals that came into vogue about a decade ago, involving both securities, like bonds, and derivatives, like interest-rate swaps.

“If they don’t reach a resolution then we get a court decision,” said James E. Spiotto, an authority on municipal bankruptcy with the law firm of Chapman & Cutler in Chicago. After New York City’s brush with bankruptcy in 1975, Mr. Spiotto worked on amendments to the municipal bankruptcy code that dealt with the types of pledges that would remain in force even after a bankrupt city stopped paying its other debts. But cases have been so rare since then that the courts have had almost no chance to interpret those amendments.

The cash that the city and Syncora are fighting over comes from an unlikely source: gambling. Like many states and cities looking for additional cash in recent years, Detroit approved casino operations in its downtown and levied a tax on the take. As the city’s population plunged and its tax base declined, the casino-tax dollars became one of its most reliable revenue sources, paying about $180 million annually in recent years.

The fight over that money raises a fundamental question of whether and how a bankrupt American city, already mired in debt, can still borrow one more time to finance its day-to-day operations even as it seeks relief from creditors under court supervision. Bankrupt companies do this routinely under Chapter 11, using a tool called debtor-in-possession financing. They attract lenders by offering to pledge business assets as collateral, showing that the loans will be repaid in full, even if their restructurings fail.

Cities, by contrast, are loath to declare bankruptcy in the first place, even more so to pledge away their prized parks or public buildings. The few cities and counties that have declared Chapter 9 bankruptcy have generally used other methods to keep going while in court, and legal experts say they have not yet seen debtor-in-possession financing used in municipal bankruptcy. Detroit may be the first, depending on the outcome of the casino-tax dispute.

Both the city and Michigan’s governor, Rick Snyder, who approved the bankruptcy, have drawn heavy fire from the municipal bond industry, including underwriter banks, for the big losses now being proposed, as much as 90 cents on the dollar. But Detroit has already asked prospective debtor-in-possession lenders to submit confidential bids to help it raise $350 million — and thanks to the possible casino-tax revenue as collateral, it has been getting offers.

The city has declined to identify the bidders.

Syncora has said in court documents that Detroit has no business offering the casino taxes to anyone else, because the city already pledged the money to it. It is also suing UBS and Merrill Lynch in New York State, making similar arguments.

Part of Detroit’s troubles stem from the complex borrowing packages it is struggling to exit. Financial advisers to local governments, especially troubled ones, recommended pairing new borrowing with interest-rate swaps to reduce their borrowing costs. The packages allowed such governments to issue variable-rate debt, which had a lower initial rate than fixed, with the swaps hedging them in case interest rates rose. That made mounting debts seem more affordable. And to further reassure investors in the municipal bond markets, the complex deals could be wrapped in a bond insurance policy.

Bill Pugliano/Getty Images Downtown Detroit. The city, the cradle of America’s auto industry, filed for bankruptcy July 18.

That’s what Detroit did in 2005, and again in 2006, when it borrowed cash to put into its pension funds for municipal workers. It used two bond insurers, Syncora and Financial Guaranty Insurance, to insure the debt-plus-swaps transaction. Of the total $1.44 billion in pension-related debt, Syncora insured swaps that were intended to hedge about $800 million.

The deals have turned out to be the bane of cities, counties and school districts, however. Even though local officials entered into them in hopes of lowering their borrowing costs, the deals tended to break down during the financial turmoil of 2008, leaving the variable-rate debt unhedged and the cities paying more than they ever expected in interest and swap payments. Usually, the only escape from their swap counterparties was to buy out the contracts, with termination fees that could easily cost millions of dollars.

That’s roughly what happened in Detroit in 2009. Its swap contracts contained a provision allowing UBS and Merrill Lynch to terminate them unilaterally if the city’s credit fell below investment grade, which it did 2009. But termination at that point would have required Detroit to come up with $400 million in cash — an amount that would have bankrupted the city immediately if it had been forced to pay it. Instead, Detroit was permitted to restructure the debt, and the two banks agreed not to terminate the swaps, sparing Detroit the big fees, at least for the time being.

Syncora had also by then lost its investment-grade rating, but its position as an insurer of the deal was strengthened because Detroit pledged to make good with its casino revenue if something went wrong. But Detroit’s prospects just kept getting worse. With a Chapter 9 petition looking ever more likely this summer, it finally terminated the contracts. The terms call for Detroit to get out of the swaps for as little as 75 percent of their true termination cost — about $250 million, instead of $344 million at current interest rates. But the deal cannot go through without bankruptcy court approval. If Detroit’s debtor-in-possession financing eventually comes through, the city would use the first $250 million or so to pay UBS and Merrill Lynch.

Detroit says it has legal authority to terminate the swaps and pledge the casino money to its debtor-in-possession lenders because Syncora was not part of the 2009 restructuring. Syncora says that without the swaps, it has a greater exposure on the related debt, which is already in default, and that it has a rightful claim to the casino money.

“Bankruptcy is, unfortunately, the land of broken promises,” Mr. Spiotto said.