In this article, a novel neuro-inspired low-resolution online unsupervised learning rule is proposed to train the reservoir or liquid of Liquid State Machine. The liquid is a sparsely interconnected huge recurrent network of spiking neurons. The proposed learning rule is inspired from structural plasticity and trains the liquid through formation and elimination of synaptic connections. Hence, the learning involves rewiring of the reservoir connections similar to structural plasticity observed in biological neural networks. The network connections can be stored as a connection matrix and updated in memory by using Address Event Representation (AER) protocols which are generally employed in neuromorphic systems. On investigating the 'pairwise separation property' we find that trained liquids provide 1.36 $\pm$ 0.18 times more inter-class separation while retaining similar intra-class separation as compared to random liquids. Moreover, analysis of the 'linear separation property' reveals that trained liquids are 2.05 $\pm$ 0.27 times better than random liquids. Furthermore, we show that our liquids are able to retain the 'generalization' ability and 'generality' of random liquids. A memory analysis shows that trained liquids have 83.67 $\pm$ 5.79 ms longer fading memory than random liquids which have shown 92.8 $\pm$ 5.03 ms fading memory for a particular type of spike train inputs. We also throw some light on the dynamics of the evolution of recurrent connections within the liquid. Moreover, compared to 'Separation Driven Synaptic Modification' - a recently proposed algorithm for iteratively refining reservoirs, our learning rule provides 9.30%, 15.21% and 12.52% more liquid separations and 2.8%, 9.1% and 7.9% better classification accuracies for four, eight and twelve class pattern recognition tasks respectively.