Dragons have all sorts of strange and powerful magic, and one of those hidden arcane secrets is the ability to split their soul into many fragments. First, they would hatch a kobold from an egg formed from kobold-ore, which cannot be smelted by ordinary mortals as it poisons those who try. But this is no problem for the right sort of dragon.
Then, with their soul split among the kobolds, when slain by a rival dragon or meddling adventurers, the kobolds could split up and regroup elsewhere, and then birth a dragon-egg to be reborn in. Some dragons realized their kobold-bodies are useful to keep around, with their small size and hands suitable for crafting.
These kobolds can communicate loosely telepathically, being all parts of the same being. It is for this reason that sometimes you might encounter kobolds that somehow seem to be acting in unison even if they couldn't possibly be talking, that seem unconcerned if individual kobolds die, because they have no sense of themselves as individuals. A dungeon full of such beings can be as hard to fight as if they were a single dragon.
It is hard to hold such a collective entity together as one mind, however. If enough individuals die all of a sudden, or if they become geographically separated, or even if enough time passes, these kobolds forget how to be one dragon and start becoming many kobolds. Their descendants will truly be separate individuals instead of getting another fragment of dragon-soul, left with only a vague memory of dragons and a tendency to work cooperatively.
To many an arrogant and rapacious dragon, giving up their rightful roles of rulers of the world to live a quiet life in a village somewhere, among family and friends, like the creatures of flesh and blood that scurry at their feet, is a truly horrific fate. But while some kobolds strive to become dragons again, or to seek out dragons, many no longer care all that much. They have their lives, and the dragons have theirs.
Some dragons are curious about ordinary mortals, and even friendly towards them, and such a dragon might split into kobolds to live among the common people and better understand their lives. Perhaps one day you'll find a caravan of kobold merchants who all talk together in unison and seem more interested in understanding your customs than actually selling anything.