Wireless sensor networks (WSNs) have been widely applied in many monitoring and surveillance processes. Due to the limited onboard energy resources, the operation of a WSN is severely hindered by its shortened lifespan arising from energy depletion. In order to alleviate this problem, and with the possibility of partitioning sensing workloads, the divisible load theory (DLT) can be adopted to derive a proper workload assignment scheme. However, special considerations have to be paid for its generic applicability in feasible workload assignment for WSNs. In this paper, an examination of DLT based WSN operations including the effect of assignment, measurement, and report times is presented, and the problem of negative workloads inherently generated in some schemes is revealed. Furthermore, by making use of the negativity phenomenon, an active-sleep scheme is proposed for the WSN such that sensor energy consumptions can be reduced and consequently extend the WSN operation lifespan. Specifically, sensors with smaller amount of residual energies are put into the sleep mode when the assigned workloads are negative. On the other hand, positive workloads are normalized and reassigned to sensors with larger amount of onboard energies. Simulation studies are carried out to demonstrate the negative workload phenomenon, and satisfactory performances of the proposed active-sleep scheme are verified.