Getting funding to keep the machine running is relevant for Katie personally, so she can keep experiencing the sight of Forest even though he's dead in her universe.
On the other hand, Lyndon proved that the multiverse theory is correct, so there are actually multiple universes where all possible different outcomes happen. So while Katie mourns Forest's loss, Forest and Lily are still alive in many alternative universes, but not the one in which they died and Katie asks the senator to keep the machine running. So I would say it's irrelevant to keep the machine running to keep them alive, cause we know they're alive in other universes, but it's relevant for Katie so she can keep seeing Forest.
In a different interpretation, we could say that the machine, once completed, is now God (Deus), and can guarantee everyone's resurrection by uploading their consciousness at the time of their death into the system. Determinism was proven wrong (confirmed by Lily's "original sin" of disobedience), so the machine cannot actually correctly predict the future, just one of the possible versions of the future, every time somebody makes a "real" decision the universe splits into multiple versions. In the end everyone will live forever in the simulation, and the simulation has to keep running while people's consciousness in the simulation will keep making decisions and altering the future of what happens in there.
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