Bit of a weird one, but here goes. Say there is a human society whose diet is 100% the human flesh of their own members. Would this society be able to maintain replacement population, or even shudder grow? I suppose figuring this out would require daily caloric requirements, caloric value of human flesh, length of gestation, average age and a host of other variables, but is there some economic principle to short-cut to a solution here? Apologies if you've been sick.
No, an animal population that subsist solely by consuming its own members is not sustainable. This is easy to see because there's no external energy input into the population (all energy comes from other members of the same population), yet the individuals will necessarily expend some energy in their metabolism (turning it into heat). Eventually, if the population cannot find any other food sources, the individuals will die (and be consumed) one by one, until the last one will run out of food and starve.
That said, there are animal populations in nature where some of the individuals may subsist almost entirely on cannibalism. This is typical of e.g. fish, which are very tiny when born, grow gradually over their lifetime, and tend to consume prey smaller than themselves. Thus, in small lakes that happen to host only one species of fish, it's not uncommon for the large adult fish to mostly eat smaller juvenile fish of the same species (which in turn eat plankton and invertebrates, providing an external source of energy to the system).