This paper addresses the problem of the brain's critical behavior in the case of a brain injury such as a stroke. Employing network models to simulate the post-stroke brain, we demonstrate that an anomalous behavior of the critical characteristics, the second-largest cluster size, results from the loss of integrity of the network, quantified within the graph theory, and not from genuine non-critical behavior. Thus, even in a post-stroke state, the brain dynamics remain critical. The proposed interpretation of the results is confirmed with the analysis of the real connectomes acquired from post-stroke patients and the control group. The results presented refer to neurobiological data; however, the conclusions reached apply to a broad class of complex systems for which a critical state is identified.