Have you heard of the Stung Series? Where almost everything dies out because of a 'bee flu'? Might be useful. Of course, in that case, you have normal humans and infected 'beast-like' humans, and not absolutely everything was wiped out... But the fundamentals might be the same. In the case where completely all other flora and fauna are gone, there may be other problems than simply cannibalism.
First, malnutrition and disease, because human meat, like other animal meat, contains mainly protein, and may not contain the minerals, vitamins and plant-based fibers needed for proper digestion, etc. You know how constipated you get if you don't eat enough fruits & veggies? Well, imagine that, multiplied by like a billion. Plus, the vitamins that help us from getting sick primarily come from plants. I don't know currently if there are any other sources of such fibers and vitamins for humans, but if we have to resort to eating each other, then we'll have widespread bowel problems and most of us would be unable to repel even simple illnesses.
Second, 'animalisation' of the weaker/less fortunate humans. Cockfighting and Dog Fighting are examples of how humans currently use animals to satisfy their violent urges. If animals were to be taken from us, it is likely that the weaker/less fortunate humans would end up in rings, forced to fight against one another, like the old gladiator times.
Third, unbalanced populations. Most females have monthly visitors that are excruiciating and debilitating. Another side to this is that women lose vitamins, and other essential nutrients much faster than men, simply because they lose blood every month. It is a contributing factor to why women get arthritis more than men in old age: because they keep losing nutrients like calcium every month. Thus, women would fall sick and die more than men in this dystopia, causing population problems. Women become a valuable resource: almost like an extinct species, and you'd have more cases of women being kept simply for sex. Not to mention procreation problems.
Fourth, environment and climate changes, and in the extreme, complete suffocation of the earth. Plants are Earth's lungs. Without them, we'd soon run out of oxygen. I suppose humans could be kept in giant sealed cities, where oxygen can be produced in limited quantities using chemical reactions. But then that means everything outside those cities would be completely inhabitable.
The list goes on...
Another probable case study could be Snowpiercer, where practically everything outside of a controlled environment is dead, and people in the lower orders do turn to cannibalism when desperate. Governance is definitely a problem, where the heros of the story rebel against the authorities. No need to wait for a decline of power.