Long term survival of the species by means of cannibalism is simply not possible. Without any other mechanism to put energy in the system it is simply not sustainable. The stronger will eat the weaker and then the last remaining will starve to death. Although a vast population spread over a large area could take quite a while before complete extinction.
Consider that even on Earth, with its countless species of life, there is no such thing as a self-sustainable ecosystem. For the vast majority of ecosystems on the planet, save for deep sea creatures, 90% of the energy actually comes from the outside - namely that is solar radiation, a.k.a sunlight. A simplified foodchain energy pyramid puts every step of the pyramid at an order of magnitude less energy content. Meaning that plant matter constitutes only 10% of all incoming solar radiation energy, primary consumers only 10% of plant matter, and so on.
Now, eliminate every other food source save for cannibalism. It will probably be worse than 10x decrease, for the sake of simplicity assume that a predator reaches maturity in 2 years, and all predators are cannibalized at that age, it would take on average consuming 1 member of the species monthly for 2 years, or 24 in total for the system to produce another "ready to eat" adult animal.
Now, if you have a 24 fold decrease for every iteration, it is quite obvious that sustainability is entirely out of question, and you have an example population size, it is trivial to calculate how many generations it will take until extinction. Let's assume a rather numerous population of 1 million:
gen 0 - 1 000 000
gen 1 - 41 666
gen 2 - 1 736
gen 3 - 72
gen 4 - 3
In just 4 generations, or 8 short years that population will be reduced to only 3 individuals, which will have quite the dilemma - breed or eat, presuming you still have members of both genders, and of with the prospect of no more food whatsoever.
In reality it will be even worse, much, much worse than the theoretical worse, because younglings will have a really hard time taking down adults, and parents will have higher energy expenditures and less chance overwhelming another adult to feed themselves and their offspring until it is large enough to hunt. It will be far more likely that adults consume the young, because of the energy disadvantage their parents are put into. There will be a lot less additions to the population than the theoretical number and extremely slim chance than any newborn reaches maturity. In practice, it will be nothing short of a miracle if the population is not completely extinct in 5 years or less.
If a plausible scenario is desired, then there must be another food source, one that is of very low efficiency, requiring a lot of effort to obtain food with very low nutritional value.
This also offers additional plot directions, as the population will gradually diverge into a cannibal group that seeks the high stakes, risking their lives to obtain high protein meat, and a group that is more like herbivores, although they can go for insects or microorganisms or some symbiotic relation with other species of life that can still provide nourishment. Depending on the environment setting, both groups could develop either collective or individualistic behavior and grow more and more distinct.
The divergence can be either a conscious choice or a product of evolution. A subset of the species might not be able to extract nutritional value from a source other than meat.
Another possibility is that younger individuals, being smaller and more nimble and agile, might be able to catch food that older, larger and slower individuals might not. But that's not very sustainable IMO.
It could also be the reverse, as individuals age, they might acquire traits and skills to obtain food from alternative sources. For example growing external physical features with the properties of a net that can trap large enough quantities of insects or microorganisms (like a whale does with plankton) to be a viable source of food for a long term survival. The older an individual grows, the more calories it can obtain, allowing it to grow in size significantly, to the point of becoming a high value target for a pack of younger individuals that will be required to take it down. With age individuals might also develop glands that produce chemicals that attract more of their foodstuff.
That sounds fairly sustainable, the young will initially be breast-fed up to a point, after which they will be forced to prey on one another, as they wouldn't really pack enough force to take down an adult, in a process of natural selection that will allow only the strongest to reach physical size large enough, so that they can take down adults by forming packs. And only the most successful members of each pack would be able to reach adulthood when they can attain self-reliance by developing capabilities to access another food source, and over time become prey to the subsequent generations.