You’re relocating to a home with security alarms
A new home may come with an installed home security system. All the alarms and cameras work, are hung in the right areas, and are ready to go. In this example, just turn on the phone to call and start a new contract. A Vivint expert will still show up to ensure there are no integration problems, and they could offer ideas on where you should replace bad outdated components. It's a preliminary trip, and you can have your alarm monitoring set up without worrying about any new components -- unless you add on.
The previous owners can move an existing Vivint contract to your family for a small set-up cost to make the process easier. If the outgoing residents are moving to an apartment complex or smaller home, you keeping the home security service might be a condition of the sale.
You need to move and bring your existing equipment with you
You might want to bring your existing Vivint system with you to a new home when you move. It should be fairly simple to do, as modern alarms and smart devices are plug and play. You can uninstall each alarm or camera yourself or call a Vivint expert to come and take care of your devices. Then a pro will set up the same components -- and any smart devices you need to add -- in your new house. Your home security contract will stay the same.