I mean her old phone is dying and her contract is up. I just want to know if I can take her new phone into Verizon. Didn't know if I had to buy the phone at Verizon
Yes, you can activate the new phone and remove the old phone that is no longer working. You can try and remove the SIM card from the current "broken" phone and if it's the same size the iPhone needs, just put the SIM card in and you're all set. If the iPhone needs a new SIM card you'll have to go into the store.
You can switch phones on your account even if the contract isn't up. Just make sure to visit a Verizon Corporate store if you aren't able to move the SIM card to activate the iPhone. The corporate store will activate the new SIM card and it will be free.
IF she bought the phone at full price on Apple's website, and it was sold as a Verizon compatible phone, you can activate on her line anytime. it doesn't matter if she is eligible for upgrade or not in the situation you desribe. It won't use her upgrade. Make sure she gets the month to month discount since she is out of contract.