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The future sixth generation (6G) of communication systems is envisioned to provide numerous applications in safety-critical contexts, e.g., driverless traffic, modular industry, and smart cities, which require outstanding performance, high reliability and fault tolerance, as well as autonomy. Ensuring criticality awareness for diverse functional safety applications and providing fault tolerance in an autonomous manner are essential for future 6G systems. Therefore, this paper proposes jointly employing the concepts of resilience and mixed criticality. In this work, we conduct physical layer resource management in cloud-based networks under the rate-splitting paradigm, which is a promising factor towards achieving high resilience. We recapitulate the concepts individually, outline a joint metric to measure the criticality-aware resilience, and verify its merits in a case study. We, thereby, formulate a non-convex optimization problem, derive an efficient iterative algorithm, propose four resilience mechanisms differing in quality and time of adaption, and conduct extensive numerical simulations. Towards this end, we propose a highly autonomous rate-splitting-enabled physical layer resource management algorithm for future 6G networks respecting mixed-critical quality of service (QoS) levels and providing high levels of resilience. Results emphasize the considerable improvements of incorporating a mixed criticality-aware resilience strategy under channel outages and strict QoS demands. The rate-splitting paradigm is particularly shown to overcome state-of-the-art interference management techniques, and the resilience and throughput adaption over consecutive outage events reveals the proposed schemes contribution towards enabling future 6G networks.