She had a son whom inherited the throne, named Cassynder Septim. It's also noted that the Septim's have long ruled the City of Wayrest as a King and when the need has arrised they've always been able to locate cousins.
then it's possible the Amulet was passed to her son.
there is also another theory:
in the book you linked, Talos has his throat slit by a High Rock assassin. He survives, but from that point on can no longer us the thu'um. It could be, that this silence damaged not only himself, but the entire Septim bloodline as well, denying them the inherent ability to use The Voice. I have my doubts about the any royalty argument, mainly because it was only the septims with the amulet together that blocked the oblivion gates. While I may concede that any royalty could wear it, I would argue that the amulet could only function on a Septim, or a dragonborn.