Spiking neural networks (SNNs) have shown a potential for having low energy with unsupervised learning capabilities due to their biologically-inspired computation. However, they may suffer from accuracy degradation if their processing is performed under the presence of hardware-induced faults in memories, which can come from manufacturing defects or voltage-induced approximation errors. Since recent works still focus on the fault-modeling and random fault injection in SNNs, the impact of memory faults in SNN hardware architectures on accuracy and the respective fault-mitigation techniques are not thoroughly explored. Toward this, we propose ReSpawn, a novel framework for mitigating the negative impacts of faults in both the off-chip and on-chip memories for resilient and energy-efficient SNNs. The key mechanisms of ReSpawn are: (1) analyzing the fault tolerance of SNNs; and (2) improving the SNN fault tolerance through (a) fault-aware mapping (FAM) in memories, and (b) fault-aware training-and-mapping (FATM). If the training dataset is not fully available, FAM is employed through efficient bit-shuffling techniques that place the significant bits on the non-faulty memory cells and the insignificant bits on the faulty ones, while minimizing the memory access energy. Meanwhile, if the training dataset is fully available, FATM is employed by considering the faulty memory cells in the data mapping and training processes. The experimental results show that, compared to the baseline SNN without fault-mitigation techniques, ReSpawn with a fault-aware mapping scheme improves the accuracy by up to 70% for a network with 900 neurons without retraining.