Long story short, once your two-year contract is up, you're essentially going month-to-month. In theory, Verizon *could* at any time, drop your service as just easily as you could drop them, since their is no long-term contract on either side. They have not publicly announced any plans to do so, but you should know going in that it is a possibility.
Up until now, I've never know them to do this, and frankly, I think what will eventually happen is rather than actually force existing grandfathered unlimited customers to change plans or cancel their accounts, they'll instead "freeze" the accounts and stop allowing customers to activate new phones on older unlimited plans, which will force many to eventually upgrade or switch.
Back before the smart phone days, they used to do this all time...you'd go to buy a new phone with new features (i.e. a camera) and they'd say, "well, that phone isn't compatible with your current plan...so you'll either have to upgrade to our new America's Choice plan or keep using that old piece of junk you already have"