The trade-offs between storage and repair traffic for replacing failed storage nodes with new nodes (newcomers) in data centers with an omniscient controller are well understood. However, in edge storage settings, newcomers are not readily available, necessitating resilient data storage (caching) without newcomers. Edge storage nodes can often communicate via a broadcast wireless medium, which can be exploited to reduce the transmitted repair traffic via network coding. Repairs for resilient distributed caching without newcomers over a broadcast medium with Random Linear Network Coding (RLNC), which does not require an omniscient controller, have not been previously studied. We develop an information-theoretic model to characterize the theoretically achievable trade-offs between stored data and transmitted repair data in the RLNC broadcast setting without newcomers. Specifically, we formulate an Information Flow Graph (FG) model and identify all cuts in the resulting FG. We validate the theoretical FG model with simulations that demonstrate that the practically achievable trade-offs are close to the theoretical trade-offs.