The Agnellis are often hailed as Italy's unofficial royal family but at the wrought iron gates of Fiat's sprawling Mirafiori plant, the worry is that their car empire is finally slipping from their grasp.
Hurrying home after a shift on the plant's long assembly lines, Fiat workers expressed concern and some resignation at the decline of Italy's most famous industrial symbol and the chance it might end up a unit of General Motors Corp.
"We're at risk if we end up in GM's hands," said one of the plant's 17,000 workers who asked to be identified only as Marco.
"The Agnellis always stood by the firm in times of crisis but we know GM shuts down companies that don't make a profit. If they close Mirafiori they'll turn Turin into a dead city," he said as he headed out onto the six-lane Corso Giovanni Agnelli boulevard, named after Fiat's 19th-century founder.
Fiat was once Europe's biggest auto maker. In its heyday Turin woke and slept in time to the assembly line shifts, and the tram network, which still criss-crosses the city, was mapped around its car plants, said local historian Giovanni De Luna.
In the 1950s and 1960s, when an estimated 400,000 migrants were drawn to Turin, new neighbourhoods of housing blocks sprung up around the city's elegant centre which was once, briefly, the home of Italy's now exiled royal family.
Fiat still ranks as one of the world's biggest auto makers, operating plants from Brazil to India and China.
But a steady slump in demand for its cars, growing losses and more than 30 billion euros ($28.17 billion) in debt have left it scrambling to sell parts of the Fiat group and cut jobs.
Analysts say the Agnellis may be forced to exercise an option to sell Fiat's remaining 80 percent of the group's core car division Fiat Auto to GM in 2004. GM already has 20 per cent.
Losses at Fiat Auto, including the Alfa Romeo and Lancia marques but not Fiat's sportscar unit Ferrari, pushed the group into the red by 529 million euros in the first quarter alone.
A new chief executive at Fiat Auto is battling to reverse the slump, promising a return to profit by 2004 and new models which break a perception that Fiat cars must be cheap.
But many people in Turin say Fiat's real priority is to whip Fiat Auto into some kind of shape before selling it to GM.
Already this year Fiat, which employs around 100,000 people in Italy, has announced nearly 3,000 job cuts, more than half of them in Turin. Separately, a survey by a small business association found 9,000 of 73,000 jobs at suppliers and other firms serving Fiat in the area were at risk from the slump.
While the prospect of Fiat without cars is an anomaly to most Italians - the group's other interests range from power to insurance and publishing - officials in Turin are facing up to the possibility that Fiat Auto might be sold.
Mayor Sergio Chiamparino said Turin was no longer a "one company town" after Fiat shifted much of its output to Italy's lower-cost south and abroad and service industries sprang up.
Fiat employs about 43,000 people in Turin, down from more than 100,000 in the 1970s.
The mayor also told Reuters that any Fiat Auto sale might turn out to be positive, saying GM could capitalise on the region's know-how and make Turin its European base, absorbing its Adam Opel division in Germany, which is also making a loss.
"The possibility should not be seen as some kind of sword of Damocles hanging over Turin," Chiamparino said. "There shouldn't be a feeling that we're in a countdown to 2004 when the hearse comes along to take away the dead."
Garel Rhys, head of an automotive research unit at Cardiff University, noted successful takeovers by GM's rival Ford of Britain's Jaguar and Volvo of Sweden, showed US majors were not only interested in asset-stripping acquisitions.
"It's not just a question of moving in and selling off the assets," he said. "GM know that if Fiat cars are no longer produced, Italians will not suddenly start buying GM cars."
Fiat officials flatly reject the persistent speculation that the group has already decided to sell Fiat Auto in 2004 and that it might seek to bring forward the sale option date.
That speculation hit fever pitch in May when Gianni Agnelli, the ageing family patriarch and the group's influential honorary chairman, flew to the United States for prostate treatment.
Agnelli is widely seen as the biggest opponent to any sale of the car maker set up by his grandfather and rumours that he had died briefly boosted Fiat's battered share price.
Agnelli returned to Turin in early June. Despite his fragile health, the white-haired octogenarian remains a powerful figure in Turin and is widely credited for the city's triumph in securing the 2006 Winter Olympics.
But his influence in the corridors of power in Rome has waned and the centre-right government of Prime Minister Silvio Berlusconi has so far offered only limited support for Fiat in the development of environmentally friendly cars.
That is a far cry from the huge incentives for Italians to buy new cars, as well as protection from foreign rivals, provided by past governments to help Fiat.
Fiat has also alienated one-time investment bank ally Mediobanca by leading an assault last year on its key industrial asset Montedison, widely seen as a triumph for the Agnellis but which also added to the group's debt woes.
In late May, Fiat was still able to persuade creditor banks to provide a lifeline in the form of three billion euros in emergency credit and stave off a rival plan which, according to news reports, was being plotted by Mediobanca.
But banks may end up with equity stakes, weakening the grip of the Agnellis, if Fiat misses its debt-reduction targets.
Adding to an end-of-era mood in Turin, Gianni's younger brother Umberto conceded in May that the Agnellis' stake in Fiat might be cut and the car unit might have to be sold.
Historian De Luna said Turin without the Agnellis in charge of Fiat cars would be a big blow to the city's sense of self.
"The idea of the city without Fiat is still impossible to contemplate," he said. "But the only way out for Fiat will be the sale (of Fiat Auto) and there's no guarantee of industrial continuity with that."
Back at the Fiat plant, Communist Party volunteers were trying to muster support for a protest march calling for state aid for the group, and many workers were willing listeners.
"People are worried in there," said Rocco, a car assembler. "The Americans aren't going to want to keep all of us. They probably only want the best bits of the company."
But others saw it differently, including Anna who was out-of-pocket, working only one week in four as Fiat cut output.
"It makes no difference to me if I work for Italians or for foreigners," she said, heading home in her white Fiat Panda car. "As long as they offer me work, it would be fine by me."