Geant4 has been used throughout the nuclear and high-energy physics community to simulate energy depositions in various detectors and materials. These simulations have mostly been run with a source beam outside the detector. In the case of low-background physics, however, a primary concern is the effect on the detector from radioactivity inherent in the detector parts themselves. From this standpoint, there is no single source or beam, but rather a collection of sources with potentially complicated spatial extent. LUXSim is a simulation framework used by the LUX collaboration that takes a component-centric approach to event generation and recording. A new set of classes allows for multiple radioactive sources to be set within any number of components at run time, with the entire collection of sources handled within a single simulation run. Various levels of information can also be recorded from the individual components, with these record levels also being set at run time. This flexibility in both source generation and information recording is possible without the need to recompile, reducing the complexity of code management and the proliferation of versions. Within the code itself, casting geometry objects within this new set of classes rather than as the default Geant4 classes automatically extends this flexibility to every individual component. No additional work is required on the part of the developer, reducing development time and increasing confidence in the results. We describe the guiding principles behind LUXSim, detail some of its unique classes and methods, and give examples of usage.