I have a Verizon plan and would like to replace one of the phones without losing my unlimited data plan. Ideally I'd like to go through a 3rd-party site since Verizon charges more for the same phones. What are the restrictions here? What phones are eligible for this? Could you please explain how that is done?
A third party site (like Wirefly, Amazon, etc) is only a reseller and will renew your contract for 2 years, and in the process your unlimited data will go away. In addition, there are added restrictions (such as NO changes to the plan within the first 180 days, an ETF for cancelling or changes on top of Verizon's ETF, etc) on many of the third party sites.
As correctly stated, the only way to keep unlimited is to purchase the phone at full retail or from a private party via ebay or craigslist or classifieds or whatever so that there is no contract renewal, and you remain month to month with your unlimited plan.