It could be the most expensive art sale ever. So expensive, in fact, that no-one even knows how much it could make. The multi-billion dollar collection of the Detroit Institute of Art (DIA), packed with masterpieces by Rembrandt, Picasso, Degas, van Gogh, and many other painters, as well as sculpture, furniture and ancient Greek pottery, is under real threat of ending up under the auctioneer’s hammer.

Despite a chorus of disapproval, Christie’s has been called in to put a price on part of DIA’s holdings, which comprise thousands of items. Just 40 of them, the greatest treasures, could be worth an eye-popping $2.5 billion, according to the Detroit Free Press.

Why? Because the city of Detroit is on the brink of bankruptcy, with an estimated $18 billion in debts. So it is looking at all its assets – which include the art – to see what it can sell off.

Detroit is an extreme, and tragic case: the art is literally irreplaceable. While its case is unique – the sale is by no means a done deal, and would be to pay the city’s debts, not the DIA’s own – it comes amid a mounting tide of museum disposals around the country.

With museums staring at falling incomes and rising costs, the temptation to raid the basements is getting stronger. Also driving the trend is the current fashion for hip contemporary art: this month the Pennsylvania Academy of the Fine Arts announced it was off-loading one of its two paintings by Edward Hopper, to kick-start an acquisition fund for – you guessed it – contemporary art. So Hopper’s East Wind over Weehawken, is going on the block at Christie’s in December, with an estimate of $22m-$28m. Poignantly, the bleak street scene from 1934 features a sign scrawled in scarlet letters in the foreground – “For Sale”.

Sale of the century

Such disposals have been happening for years. To howls of disapproval, in 2007 the Albright-Knox museum in Buffalo, New York, sold some of its prize historic treasures to concentrate on what director Louis Grachos called its core mission, buying and showing the “art of the present”. A Roman period bronze sculpture of Artemis and the Stag was hammered down by Sotheby’s New York for a lusty $28.6m.

Since the financial crisis, such sales have accelerated sharply. In 2011 alone, the Cleveland Museum of Art, the Getty Center in LA, the Art Institute of Chicago and the New Jersey Historical Society all sold works at auction. In February this year, the Metropolitan Museum of Art dumped 16 Old Masters at Sotheby’s, raising $2.4m, including $626,500 for a portrait by a follower of Rubens.

In Europe, museum disposals are far rarer, in some countries, such as France, they are forbidden by law for works in national collections. In general, museum associations require that if works are sold, then the money raised must go towards other acquisitions rather than just fixing the plumbing. The global authority, the International Council of Museums is clear: “Museum collections are held in public trust and may not be treated as a realisable asset,” it states.

The arguments against such sales are many and convincing, with the notion of “public trust” being crucial: museums must be seen and trusted as institutions that are not blown here and there by the winds of fashion or by commercial considerations. The Hermitage Museum in Russia disposed of swathes of masterpieces in the 1930s, to ease its dire balance of payments problems; in the 1950s, Minneapolis became infamous for selling thousands of paintings, antiquities and Asian works of art. New York’s Metropolitan Museum of Art caused an international scandal in the 1970s when it booted out Van Gogh, Modigliani, Picasso, Renoir and other works to buy David Smith and a Richard Diebenkorn. None of those institutions could afford to buy back those works now, even if they were available.

Another argument against selling off art is that it might deter future donors from gifting works, if they might one day end up in the saleroom. A few years ago a New York museum put up for sale a David Smith sculpture without even bothering to consult the donor – who was alive, well and furious when he heard it was going under the hammer. (The museum hastily backtracked and withdrew the work from auction.)

Upstairs, downstairs

There is, of course, a counter argument to all this. Museums are not stuffed with masterpieces – far from it. Most have a few highlights and vast troves of works that are in poor condition, duplicates and never on show. Even the exacting American Association of Art Museum Directors accepts sales when there is an effort to “refine and improve” a collection.

Even when works sold by museums are substandard, they command premium prices, thanks to the prestigious label of the institution – even if no longer wanted. The auction houses are frantic to sell any cast-offs, knowing that buyers will be prepared to push up prices more than for a work without such a provenance. In the case of Detroit, with its tip-top collection, any sale would be sure to shatter the record books.

Still, many fear that the current round of disposals might prove short-sighted. There is increasing pressure on museums to show flashy new art, to bring in a new, younger and more diverse public. But contemporary art prices are at an all-time high, forcing institutions to dig deeper into their pockets to acquire what may  prove to be today’s firework, but tomorrow’s damp squib – and an expensive one at that.

If you would like to comment on this story or anything else you have seen on BBC Culture, head over to our Facebook page or message us on Twitter.