Was the Cardassian Union dissolved after the Dominion War, or did it continue to exist? Who was put in charge of rebuilding Cardassia? Was it Damar? I only ask because Damar mentions to Kira after killing Rusot that "[Rusot's] Cardassia is dead, and it isn't coming back" in the episode DS9 episode "Tacking Into the Wind". In the last episode of DS9, Garak also talks to Bashir about "his" Cardassia no longer existing. Did Cardassia actually change from its old ways after the Dominion War, and become a more progressive society? Any researched answer or even speculation would be appreciated.
Different EU novels present potential fates for the Cardassian Union.
The most obvious references is "A Stitch in Time" by Andrew J. Robinson (the actor who played Elim Garak). In it, we see that Cardassia Prime has suffered enormous losses of both population and infrastructure with almost all major cities having suffered catastrophic assaults from ground and orbit. The government is being rebuilt along democratic lines (with someone named Alon Ghemor at the head of a movement known as the Reunion Project). At the end we see that the planet is beginning to come back to some semblance of normality.
"Someone once said that democracy was the flawed solution to a perfect mess . . . and I absolutely agree. The Reunion Project won a majority in four of the six sectors, and instead of being able to impose their will on the political situation, everything is discussed endlessly . . . and then put to yet another vote! Is this your vaunted democracy, Doctor? To be subjected to the opinion of any person who has the breath to utter one? How does anything get accomplished? If this is—as some fervently believe—a Federation plot to diminish Cardassian involvement in the quadrant, then it has succeeded ingeniously. We’re much too involved in discussions over power grids and waste disposal to care about anything else."
You've also got the much more gloomy fate seen in Millennium : Inferno, in which the Cardassian people have suffered nothing less than their complete and utter destruction:
"The survival of Cardassia?" Cardassia's defeat was the gravest event Garak the tailor could imagine. Nothing meant more to him than his world and his people, despite the flawed leadership that currently blighted both.
"Even graver, I'm afraid," the visitor replied. "Though I have seen … I have seen Cardassia Prime laid waste and our people … our people erased from existence."
Since anything not shown on screen (movies/TV series) is going to be soft-canon for Star Trek you can pick and choose what you like. Here is Star Trek Online's version of what happened:
(Whether the game itself is 'good' or not should be a separate matter.)
From STO wiki: Cardassian Union
Post-War crises and reconstruction efforts (2379-2385)
- Following the Dominion War, Cardassia Prime plunges into an economic crisis. (2379/2380)
- The Cardassians refuse to extradite members of their government and military to stand trial for war crimes committed during the Dominion War and the occupation of Bajor. (2381)
- In 2382, 472 Cardassians from the Bajor coalition's war crimes list disappear from Cardassia Prime within four months.
- In the following year, Cardassia Prime is swept by a resurgence supporting religion and spirituality.
- Although the Federation Council and the Union support leaving the established borders of the Federation-Cardassian Treaty of 2370, the Bajor coalition demands the Cardassians to surrender colonies granted to them in the treaty. (2385)
- Meanwhile on Cardassia, the U.S.S. Pasteur supports the reconstruction of medical facilities and hospitals.
Path of redemption and democratization (2386-2392)
- A new treaty between the Union and the Federation is signed: While the Cardassians agree neither to field a military nor to wage war, Starfleet is assigned to protect Cardassian space if an invasion should happen. In response to the agreement, the requests for prosecution of Cardassians for war crimes is dropped by Bajor. (2386)
- The military is reformed into the smaller Cardassian Self-Defence Force, or CDF, the following year. In addition, the CDF's operations are restricted to Cardassian space.
- A token force consisting of six ships is sent by the provisional Detapa Council to aid Romulan relief efforts following the destruction of Romulus. Concerned with the conservation of Cardassia's remaining resources, popular opinion is against this decision. (2388)
- Elections on Cardassia are supervised by the Federation. The civilian coalition led by Elim Garak narrowly defeats the hardliner faction under Gul Madred, who demand the withdrawal from the latest Federation-Cardassian Treaty and the resurrection of the military. (2389)
- Later the same year, Madred aquires rights, allowing him to mine several mineral-rich planetoids in Cardassian space. He has a large mining oeration built on Septimus.
- In 2390, Garak and the Grand Nagus of the Ferengi Alliance, Rom, sign several contracts. The Alliance returns sacred Jevonite artifacts and invests into the restart of Cardassian industrial complexes. The Ferengi receive favorable trade agreements for goods of the rebuild industry in exhcange.
- A series of reforms is signed by the Detapa Council to promote economic stabilty and a growth of population. In addition, thousands of displaced military officers are folded into civilian industries. (2392)