Understanding the survival and orbital evolution of brown dwarf (BD) companions during the post-main-sequence (MS) evolution of their host stars is increasingly important, especially with recent discoveries of many substellar companions around white dwarfs (WDs). We investigate the long-term evolution and final outcomes of BDs orbiting low-mass MS stars as these evolve into WDs. By comparing forward-modeling populations with observed WD-BD binaries, we test evolutionary models and predict the existence of yet-undetected systems. We employ the COMPAS binary population synthesis code to evolve observed MS-BD systems through the post-MS phases of their host stars into the WD stage, tracking orbital changes driven by mass loss, tides, and common-envelope (CE) evolution. Our simulations reproduce a period gap in the distribution of detached WD-BD binaries, consistent with observations. We also identify a boundary separating detached and semi-detached systems on the period-mass diagram, located at orbital periods of ~1-2 hours depending on the BD mass. We predict that a subset of currently known MS-BD binaries will survive post-MS evolution and emerge as detached WD-BD systems, while others will undergo CE evolution and potentially form cataclysmic variables with BD donors. Our results reproduce the observed period gap in WD-BD binaries and provide quantitative predictions for the role of CE efficiency in shaping their distribution. This work predicts that many WD-BD systems remain undetected, motivating targeted searches with microlensing and high-contrast imaging techniques using next-generation large telescopes.