How might a carnivorous species subsist on a cycle of cannibalism

Let's say a carnivorous species loses all available food sources, and they begin to eat one another to survive. Let us also say that prion diseases are not an issue for this particular predator. Assuming there were enough of these creatures when this practice began that they could survive through a few breeding cycles and adapt to this way of life, could such a system actually be sustainable? Or is it pure fantasy?

If possible, what kind of special physical traits, population density, behavior, etc. would the creatures need to have in order to prevent their own extinction?

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How might a carnivorous species subsist on a cycle of cannibalism

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