This paper considers the Slepian-Wolf coding based data aggregation problem and the corresponding dependable clustering problem in wireless sensor networks (WSNs). A dependable Slepian-Wolf coding based clustering (DSWC) algorithm is proposed to provide dependable clustering against cluster-head failures. The proposed D-SWC algorithm attempts to elect a primary cluster head and a backup cluster head for each cluster member during clustering so that once a failure occurs to the primary cluster head the cluster members within the failed cluster can promptly switchover to the backup cluster head and thus recover the connectivity of the failed cluster to the data sink without waiting for the next-round clustering to be performed. Simulation results show that the DSWC algorithm can effectively increase the amount of data transmitted to the data sink as compared with an existing nondependable clustering algorithm for Slepian-Wolf coding based data aggregation in WSNs.