I can't seem to get a straight answer from C Spire. I have a C Spire iPhone 7+ on 10.2. I don't like the phone, it's simply too big for me to carry in my pocket. My son as the 7 but it's on Verizon. Verizon tells us we can simply swap the sim card. C Spire says I can't. They say their phones are locked and since I'm under contract they won't unlock it for us to swap. I was wondering if I jailbreak my phone will we be able to swap? Does jailbreaking unlock it from the C Spire network?
First off, jailbreaking and unlocking are two different things.
Jailbreaking allows you to run unsigned code on your iDevice. Unlocking allows you to take your device to a different carrier.
Back in 2011, the last year you could do this, you COULD jailbreak and THEN unlock. It's called a software unlock. But you can't do that anymore because all the easy $1 third party unlocks that happened around that time killed the development. A software unlock also means that if the phone is ever restored, so is the lock status.
Second, you have an iPhone 7. Currently, the ONLY jailbreak out there for iOS 10 right now is for iOS version 10.1.1. And it's very unstable. It's recommended that only devs jailbreak right now because it's an arcane procedure still. It's inferred that there wil be a stable jailbreak later, but you never know when that will happen.
I bring this up because you can't just willy nilly decide "Oh, I want to jailbreak!" You have to be on the correct version of iOS for it. If you aren't - no jailbreak is possible.
You mention that your son has a Verizon iPhone. Verizon is correct, you can simply put your C-Spire SIM in the Verizon iPhone. That is because Verizon has an agreement with the FCC to have all of their LTE capable devices unlocked out of the box. That means your son's phone is unlocked - because it's a Verizon LTE capable device.
But you need to give your son your C-Spire phone and that's the crux of the problem. Your only option here if you do not want to pay off the phone, is to find a third party unlock service because your phone is still locked to C-Spire.
And if you could jailbreak, it wouldn't be of any benefit to you.