Network flow games model domains where a commodity can flow through a network controlled by selfish agents. Threshold Network Flow Games (TNFGs) are a form of such games where an agent coalition wins if it manages to send a flow exceeding a certain threshold between a source and a target vertex. Cooperative game theory predicts the agents’ actions in such settings with solutions such as the core, the set of stable distributions of a coalition’s gains among its members. However, some games have empty cores, so every distribution is inherently unstable. When the core is empty, one must use a more relaxed notion of stability, such as the least-core. We examine several problems regarding the least-core in general and restricted TNFGs.