We all know an impending rebadge is coming. Chances are VZ will consider those that refuse it as effectively resigning, which means no severance and no unemployment.
I'm not a lawyer, but a rebadge could also be interpreted as "your job is now at Deloitte/Infosys/HLC". That means the VZ job no longer exists. If the rebadge is declined, it could be an involuntary separation with severance and unemployment.
I'm guessing VZ would think twice should there be a lawsuit threat.
During the 2008 VSP / Infosys rebadge, VZ wasn't offering the extended severance to those eligible for retirement but relented when enough people complained. It's not the same thing and times have changed, but nothing will happen if the affected people don't push back.
Note: what happened with Daniel's "the transformation is going to be hard work, but when you look back you'll be very proud of it"? I guess the rebadge wasn't in the cards back then.