One of the masterpieces in the Detroit Institute of Arts (DIA) is James Whistler’s “Nocturne in Black and Gold.”

Ominous dark shadows are punctuated with the light of fireworks falling to Earth. It is an “urban, ephemeral, indescribable spectacle,” says the blurb. It is “a pot of paint [flung] in the public’s face,” harrumphed John Ruskin, a Victorian critic.

It could also be a metaphor for the rise and fall of Motown, not least since it is one of many works the bankrupt city may sell to pay off its debts.

Detroit has one of the finest art collections in America, including works by Van Gogh, Degas, Matisse and Bruegel the Elder. Murals by Diego Rivera, commissioned in the 1930s, show muscular workers cranking out cars in a Ford factory.

Many of those factory jobs have now left. (Some have gone to Rivera’s native Mexico.) Detroit’s population has collapsed. With a shrunken tax base, the city cannot service its debts of more than $17 billion, or $25,000 for every resident.

Desperate times call for harsh measures. Kevyn Orr, the city’s emergency manager, who was appointed this year with almost dictatorial powers to turn the city’s finances around, has ordered an inventory of the treasures in the DIA. These were valued at $1 billion in 2004; they may be worth more now. If Detroit formally declares bankruptcy, they may be sold. That would be controversial.

Many affluent suburbanites hate the idea. The suburbs that encircle Detroit are politically separate: Suburbanites neither pay city taxes nor send their kids to crumbling city schools. But they do like to visit the art museum from time to time. Only last year, they voted to pay a special tax to subsidize it.

Even more appalling, for many suburbanites, is the prospect that the proceeds would bail out what they see as a corrupt and incompetent city government. In March a former mayor, Kwame Kilpatrick, was convicted on two dozen charges, including racketeering and bribery. The City Council is in chaos: Its president has gone missing, amid allegations of an inappropriate relationship with a high-school boy. A third of the council seats are empty. Race aggravates matters. The city is 83 percent black. Adjacent Oakland County is 77 percent white, and more than twice as rich.

The DIA is unusual in that it is directly owned by the city. Art museums elsewhere are typically owned by nonprofit foundations. So whereas other struggling rust-belt cities with great art collections, such as Toledo and Cleveland, probably could not sell them to repay their creditors, Detroit probably can.

Scandalized out-of-towners are eager to prevent this. Michigan’s attorney general says that the artwork is held in trust and therefore cannot be sold. State legislators are proposing a law that would block a debt-driven sell-off. Even if Orr has the law on his side, creditors and art-buyers may be wary of getting tied up in court. Art lovers hope that the red tape that helped wreck Detroit’s economy might save its art collection.

Were the city to sell its paintings, it would lose some of its allure for residents and tourists alike. Annmarie Erickson, the DIA’s chief operating officer, argues that art can “empower all of us.” But many residents will grasp at anything that means their pensions might be paid, or the streetlights might start working again. “I earned that pension,” said Robert Jones, a retired police officer who now helps run a car park outside the Detroit Tigers’ baseball stadium.