As the Greek crisis escalated in recent days, Europe’s common currency crossed a line that could taint it forever.

The crucial moment occurred when Greece’s debt dispute with other European countries became a fight to stay in the euro. The prospect of a country leaving the currency was once unthinkable. Europe’s goal is to form an “ever closer union” — and the euro’s creators expected the currency to play a driving role in that process.

“You are the euro, and upon this currency we will build our Europe,” is how one fervent European leader put it two decades ago. But as relations between Greece and its creditors broke down last month, the currency stopped being a force for unity. In many ways, it became a weapon that each side seized upon to advance its cause.

Greece’s creditors, mostly other European countries, appeared to gain the most leverage from this tactic. Knowing that the Greek people greatly favor being in the euro, European leaders have raised the specter of an exit, in part as a way to press Greece’s government into a compromise.

The common currency became a cudgel.

Analysts are assessing the damage done to the euro, used by Greece and 18 other countries, as well as the potential for a shock to the Continent’s wider economy. A chaotic Grexit could disrupt financial markets and damp economic activity.

Still, the currency is not expected to fall apart completely. It is possible that the euro would in some ways strengthen if a Greek departure left behind a group of participating countries that got along better. Greece accounts for only 2 percent of the euro area’s gross domestic product.

Even so, many analysts say that some of the important ideals behind the euro — such as cooperation and inclusivity — have suffered a big blow.

“To be honest, the dream has died regardless of what happens with Greece, because that dream was just a fantasy,” said Jens J. Nordvig, an analyst with Nomura Securities and the author of “The Fall of the Euro.”

On Wednesday, Greece submitted a request for a new loan that expressed its intent to carry out the sort of overhauls that its creditors favor. Yet even if a deal is done, and Greece remains within the common currency, the last few months have fully revealed the potential fault lines within the euro.

The struggle over Greece could set an unforgettable precedent for the next time any country runs afoul of a European majority. “You have an incomplete currency area that is vulnerable,” Mr. Nordvig said. “It doesn’t mean it’s going to totally disintegrate, but it’s going to remain vulnerable.”

Greece’s problems show just how different the euro is from, say, the dollar. In the United States, if one region goes into a slump, it does not face being cut off from the rest of the country. The federal government usually provides fiscal support to the region without igniting a firestorm of resistance from other parts of the United States. And the Federal Reserve can make emergency loans to the banks in the region to prevent runs on the financial system there.

In Europe, the process for helping troubled countries is much more difficult and fragmented.

Greece has received some assistance from the rest of Europe, through bailouts in 2010 and 2012, and the European Central Bank has provided considerable emergency loans to Greek banks. Greece even followed through on some of the austerity measures that its creditors demanded. But after several years of hard times, staggeringly high unemployment and debt loads that remained stifling, the Greeks in January voted for a leftist government. It did not want to have to agree to more austerity to receive fresh aid, which was then going to be used to pay off a large amount of debt coming due this year and next.

The parallels are not exact, but if Greece were a heavily indebted city in the United States, things could have turned out quite differently. Greece could have filed for bankruptcy. And during the ordeal, it is highly unlikely that the city and all its banks would face the prospect of losing their access to dollars.

Greece, however, is now being deprived of fresh euros. This has caused the banks to allow only the tiniest withdrawals, and it means that Greece may soon have to introduce a new currency, which would almost certainly be worth far less than the euro. Fears of the latter may yet persuade Greece’s government to give some ground and make a deal before a Sunday deadline that Europe laid down this week.