Companies can do that because its open sourced. They get it open and they close it themselves. Android being open source doesn't have anything to do with Verizon closing down their systems. Open source means that you can get the Android source code and do anything you want to it. Also, its only the OS that's open source. The phone itself is a hardware which is technically owned by Verizon until you finish paying for it.
Basically, root your phone and flash a custom version of Android if you want to have a fresh unit.
Or buy an unlocked Nexus.