Thanks for your question. My name is ***** ***** I look forward to assisting you.
As soon as you close your Verizon service, you will lose your verizon email address. If you keep the service with Verizon, they will not close it.
But you cannot get another internet provider and use Verizon at the same time as they will need to switch you out onto the network so you would have to close the account.
What I suggest you do is get an email account that is not provider specific. This way you never run into this problem regardless of who your provider is. You can get one from Google for free for an unlimited amount of time by creating an account herehttps://accounts.google.com/signup
Then inform everyone of this new address then switch to a new provider.
This is the best method forward as once you switch to another provider, Verizon will stop allow you access to the email service.
If you would like any additional information or assistance, please do not hesitate to let me know.
And if you can take a second to rate my service by clicking one of the stars at the top of the screen or smiley faces, that would be greatly appreciated.