You moved into a house with an existing security system
Sometimes when people purchase a house, a security system is already in use. All the components function well, are installed in the right areas, and are ready to go. In this example, you might find that you have to call and start a new service contract. A Vivint installer will still show up to make sure there are no usability issues, and they could offer suggestions on upgrades. It's a preliminary trip, and you can have your monitoring set up without paying for any new devices -- unless you get some new devices.
The previous owners can give an existing Vivint contract to you for a small transfer cost to make the transfer simpler. If the previous owners are downsizing to an apartment or smaller home, you keeping the home security contract might be an addendum of the sale.
You are looking to move and bring your existing equipment with you
You might want to bring your old home security components with you to your new place when you move. It should be fairly simple to do, as most smart devices are plug and play. You can remove each device yourself or use a Vivint expert to take care of your devices. Then an expert will set up the same devices -- and any additions you want to have -- in the new home. Your home security contract will remain the same.