Increasing network utilization is often considered as the holy grail of communications. In this article, the concept of sub-rate coding and decoding in the framework of linear network coding (LNC) is discussed for single-source multiple-sinks finite acyclic networks. Sub-rate coding offers an add-on to existing LNC. It allows sinks whose max-flow is smaller than the source message-rate, termed \emph{sub-rate sinks}, to decode a portion of the transmitted message without degrading the maximum achievable rate of LNC sinks whose max-flow is equal (or greater) than the rate of the source node. The article studies theoretical aspects of sub-rate coding by formulating the conditions a node (and indeed the network) must fulfill so as to qualify as a legitimate sub-rate sink.