Recycling

You could do it with added photosynthesis, but an adult human yields about 35k (k)calories in meat excluding organs, so we can triple that for all of the usable meat. That would mean that, assuming ratios of calorie intake to body size are consistent, the animals would need to consume each other at a rate of one every other month.

With photosynthesis, this can be extended indefinitely, and there are island ecosystems that are relatively isolated. Those depend on different organisms photosynthesizing, consuming the photosynthesizers, and decomposing indigestible remains, but there are examples of plants that photosynthesize and digest flesh or algae that photosynthesize and decompose. Different types of bacteria do all three, but that doesn’t feel too close to the spirit of the question.