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Recent evidence on resting-state functional magnetic resonance imaging (rs-fMRI) suggests that healthy human brains have a temporal organization represented in a widely complex time-delay structure. This structure seems to underlie brain communication flow, integration/propagation of brain activity, as well as information processing. Therefore, it is probably linked to the emergence of highly coordinated complex brain phenomena, such as consciousness. Nevertheless, possible changes in this structure during an altered state of consciousness remain poorly investigated. In this work, we hypothesized that due to a disruption in high-order functions and alterations of the brain communication flow, patients with disorders of consciousness (DOC) might exhibit changes in their time-delay structure of spontaneous brain activity. We explored this hypothesis by comparing the time-delay projections from fMRI resting-state data acquired in resting state from 48 patients with DOC and 27 healthy controls (HC) subjects. Results suggest that time-delay structure modifies for patients with DOC conditions when compared with HC. Specifically, the average value and the directionality of latency inside the midcingulate cortex (mCC) shift with the level of consciousness. In particular, positive values of latency inside the mCC relate to preserved states of consciousness, whereas negative values change proportionally with the level of consciousness in patients with DOC. These results suggest that the mCC may play a critical role as an integrator of brain activity in HC subjects, but this role vanishes in an altered state of consciousness.