Human consciousness is widely understood to be underpinned by rich and diverse functional networks, whose breakdown results in unconsciousness. Candidate neural correlates of anesthetic-induced unconsciousness include: (1) disrupted frontoparietal functional connectivity; (2) disrupted brain network hubs; and (3) reduced spatiotemporal complexity. However, emerging counterexamples have revealed that these markers may appear outside of the state they are associated with, challenging both their inclusion as markers of conscious level, and the theories of consciousness that rely on their evidence. In this study, we present a case series of three individuals in disorders of consciousness (DOC) who exhibit paradoxical brain responses to exposure to anesthesia. High-density electroencephalographic data were recorded from three patients with unresponsive wakefulness syndrome (UWS) while they underwent a protocol of propofol anesthesia with a targeted effect site concentration of 2 μg/ml. Network hubs and directionality of functional connectivity in the alpha frequency band (8-13 Hz), were estimated using the weighted phase lag index (wPLI) and directed phase lag index (dPLI). The spatiotemporal signal complexity was estimated using three types of Lempel-Ziv complexity (LZC). Our results illustrate that exposure to propofol anesthesia can paradoxically result in: (1) increased frontoparietal feedback-dominant connectivity; (2) posterior network hubs; and (3) increased spatiotemporal complexity. The case examples presented in this paper challenge the role of functional connectivity and spatiotemporal complexity in theories of consciousness and for the clinical evaluation of levels of human consciousness.