Distributed lossless coding of correlated sources offers the potential for sizable reductions in coding rates in comparison to independent coding.  
However, it is more sensitive to encoder failures as the loss of one encoder may cause the decoding of many sources to fail.   
In the extreme case, if data from even one encoder fails to get to the decoder, due to node failure or packet loss, it may result in complete failure of the decoder to decode data of even a single node.
In this paper we characterize the trade-off between reliability, computed as the fraction of sources recovered at the decoder and efficiency, computed as the average rates of the encoders. 
We model distributed coding systems using balanced bipartite graphs, which we call {\em dependence} graphs.
Based on these graphs, we divide the systems into two categories: {\em rigid} and {\em flexible}. 
In rigid systems the decoder for a source requires a specific subset of encoder outputs to decode. However, in flexible systems, the decoder for a source can decode the given source using from multiple subset of encoder outputs.
Analyzing achievable rigid and flexible schemes we find that flexible schemes offer significant performance gains over their rigid counterparts.