Rock Band 2 (Xbox 360) enforces an Xbox Live connection for downloaded songs due to Digital Rights Management (DRM) and platform policies.
Xbox 360 Xbox Live servers are still up (as of 2024), but the marketplace is closed — no new purchases. Existing DLC works if licenses are intact. For permanent offline play, the only guaranteed path is original discs + original console (or PC mods like Rock Band 3 Deluxe on RPCS3, legally gray).