Where did you read that the carbon cycle is coming to an end?
This means that the practical end of the Earth, as far as humans are concerned, is on track not for a few billion years from now when the Sun expands—the commonly imagined end of "Earth gets charred/absorbed by the Sun"—but a few hundred million years from now. Maybe sooner for a variety of reasons, but that's likely to be the final lights-out—the upper bound—for everything but some microbes and a few lobsters around deep-sea vents or whatever. Barring some serious intervention by intelligent, technologically-advanced life, anyway.
C4 carbon fixation would already last a lot longer than C3 carbon fixation. Probably some other sources of carbon that can be found.