The starship Defiant is caught in a type of "time-bubble" above an inhabited planet. When they investigate, it is discovered that the inhabitants are the descendants of the Defiant's crew. The inhabitants have lived on the planet for many years and their own history began when the Defiant crashed with no hope of contacting the Federation or repairing the ship. Faced with that reality, the small crew of the Defiant (including Dax, Sisko, O'Brien, etc) decide to remain and establish a society.
The society presented to the crew of the Defiant includes only the descendants of the original inhabitants. The only original "colonists" are Odo, whose Changeling physiology gives him greater longevity than the rest, and the Trill symbiont Dax, in a new host, Yedrin Dax, descendant of Worf and Jadzia Dax.
The crew is forced to choose between repairing the Defiant and escaping the situation (and wiping out their descendants and everything they've built), and remaining, allowing the Defiant to crash and letting things evolve as they have been presented to them. After much discussion, they choose the latter. Unbeknownst to them, however, the future Odo, wishing to prevent Major Kira from dying, changed their flight plan. Instead of flying through the spot in the atmosphere that will cause them to be flung back in time, they escape the atmosphere, and wipe out their descendants and the colony they had built.