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Extending the idea of having silent nodes in a Wireless Sensor Network (WSN) overhear the two-way timing message communication between two active (master and slave) nodes, this paper focuses on deriving the Maximum Likelihood Estimator (MLE) and performance lower bounds for the clock offsets of the listening nodes located within the communication range of the active nodes by assuming an exponential link delay modeling. Hence, synchronization with the reference node is achieved at a very low cost. The MLE is also shown to be the minimum variance unbiased estimator of the clock offset when the mean of exponential link delays is known. Since it is attractive to know in advance the extent to which an estimator can perform relative to global performance lower bounds, the Chapman-Robbins and Barankin bounds for the clock offset estimator are derived. It is shown that for an exponential link delay model, the mean square error of the unbiased clock offset estimator is inversely proportional to the square of the number of observations, and hence its performance is on a similar scale, albeit slightly lesser, as compared to the usual sender-receiver clock offset estimator.