Gray, Radical Dreamers informs us that the Frozen Flame was inside the Mammon Machine, and that perfectly makes sence. No one but Schala could activate the machine, because she is the arbiter! How RD describes their connection proves that she is pretty much the first arbiter ever.
As for Marle's pendant, in the original timeline, Schala also used up that energy somehow and then it was lost when she died, or if she truely reincarnated herself in her own timeline, then that is the case of why it didn't go down with her.