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This work presents the design and autonomous navigation policy of the Resilient Micro Flyer, a new type of collision-tolerant robot tailored to fly through extremely confined environments and manhole-sized tubes. The robot maintains a low weight (<500g) and implements a combined rigid-compliant design through the integration of elastic flaps around its stiff collision-tolerant frame. These passive flaps ensure compliant collisions, contact sensing and smooth navigation in contact with the environment. Focusing on resilient autonomy, capable of running on resource-constrained hardware, we demonstrate the beneficial role of compliant collisions for the reliability of the onboard visual-inertial odometry and propose a safe navigation policy that exploits both collision-avoidance using lightweight time-of-flight sensing and adaptive control in response to collisions. The robot further realizes an explicit manhole navigation mode that exploits the direct mechanical feedback provided by the flaps and a special navigation strategy to self-align inside manholes with non-straight geometry. Comprehensive experimental studies are presented to evaluate, both individually and as a whole, how resilience is achieved based on the robot design and its navigation scheme.