Worgen children
By the CDev response, worgen have human children. The logic given is that curses do not pass to offspring. In lore however, curses do in fact pass to offspring, such as the Curse of Flesh, of the Sporemounds, of Seth, of Fel, Naga, and literally every race except Trolls are the result of mutation. There is also a worgen child in-game described as offspring, so it is possible by some means, either by bite, blood, or inheritance. I let my players choose for sake of story, since there is support for either argument.
- Could a female worgen give birth to a human child?
- Is there a rite of passage to become a worgen?
- The Curse: Do worgen have human offspring?
The "Cure"
As for the state of the worgen cure, there is none. All worgen hunt in the wild on all fours, and have innate instincts and boiling rage. Genn Greymane still runs and hunts on all fours with a pack, as shown in Wolfheart. What -does- exist are sedatives and medications, such as the sedative created by Oliver Harris, which is rarely effective on mindiless worgen, who he then decapitates.
The Ritual
What also exists is the Ritual of Balance, a kaldorei ritual consisting of three visions acting as an anger management session to help resolve old grudges, and thus make the rage and instincts more manageable. This too has a poor success rate, and those that fail it go mindless from their own memories, and are put down by Genn and his men in Wolfheart. Neither the medication nor the therapy session pass to young. But have no fear, the mindless state is not the default, as shown by the worgen in northrend, and Genn himself, who could shapeshift before the ritual was even created.
Will worgen die out?
That is possible, if hunted to extinction all at once, but unlikely. The silverpine and duskwood worgen are the two remaining free feral packs, one fighting the Forsaken and the other biting humans, both of whom have advocated for spreading the curse. Neither seem to be losing numbers, and quest text says the Nightbane are growing. Even in the Alliance, there are those who willingly or reluctantly seek to become worgen, like Tess Greymane and Hillsbrad Refugees. Worgen can turn humans and night elves into worgen, have now spread across the world, and can use human form to blend in if threatened. Eradication at this point is highly unlikely.
That is Werewolf: the Apocalypse lore specifically, garou are a bit different than traditional lycanthropes.