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More and more applications that require high reliability and fault tolerance are realized with wireless network architectures and thus ultimately rely on the wireless channels, which can be subject to impairments and blockages. Hence, these architectures require a backup plan in the physical layer in order to guarantee functionality, especially when safety-relevant aspects are involved. To this end, this work proposes to utilize the reconfigurable intelligent surface (RIS) as a resilience mechanism to counteract outages. The advantages of RISs for such a purpose derive from their inherent addition of alternative channel links in combination with their reconfigurability. The major benefits are investigated in a cell-free multiple-input and multiple-output (MIMO) setting, in which the direct channel paths are subject to blockages. An optimization problem is formulated that includes rate allocation with beamforming and phase shift configuration and is solved with a resilience-aware alternating optimization approach. Numerical results show that deploying even a randomly-configured RIS to a network reduces the performance degradation caused by blockages. This becomes even more pronounced in the optimized case, in which the RIS is able to potentially counteract the performance degradation entirely. Interestingly, adding more reflecting elements to the system brings an overall benefit for the resilience, even for time-sensitive systems, due to the contribution of the RIS reflections, even when unoptimized.