Caecotrophy, the same strategy rabbits use, separates two kinds of output. Firm faecal pellets, voided at night, are waste. Soft pellets produced by the caecum during daylight are rich in bacteria that have been fermenting leaf material, and these are consumed straight from the anus while the animal rests in its drey.
The payoff is the microbes themselves. Eucalyptus leaves are low in nitrogen, high in fibre and loaded with phenolics and terpenes, and a large share of the usable protein in the ringtail's diet is the bacterial biomass grown on that substrate. Passing it through the gut a second time allows those cells to be digested and absorbed rather than lost.
The timing matters more than it may appear. Eating the soft pellets by day and the leaves by night keeps the two streams separate, and captive ringtails prevented from performing caecotrophy lose condition even on the same leaf diet, which is direct evidence that the second pass is doing real nutritional work.