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Neuromorphic computing is emerging to be a disruptive computational paradigm that attempts to emulate various facets of the underlying structure and functionalities of the brain in the algorithm and hardware design of next-generation machine learning platforms. This work goes beyond the focus of current neuromorphic computing architectures on computational models for neuron and synapse to examine other computational units of the biological brain that might contribute to cognition and especially self-repair. We draw inspiration and insights from computational neuroscience regarding functionalities of glial cells and explore their role in the fault-tolerant capacity of Spiking Neural Networks (SNNs) trained in an unsupervised fashion using Spike-Timing Dependent Plasticity (STDP). We characterize the degree of self-repair that can be enabled in such networks with varying degree of faults ranging from 50 to 90% and evaluate our proposal on the MNIST and Fashion-MNIST datasets.