The way it is supposed to work, when you register to vote after having moved to a new state, you are supposed to be asked for your old voting address. The new state is supposed to send notice that you are newly registered in a new state to your former (old) state. 

This is how your name is purged from the voter rolls at the last location. 
Source : usa.gov/register to vote
"You can’t vote in more than one place. When you register to vote in a new location, you’ll be asked for your previous address. Your new election office will send a cancellation form to your previous election office."

At a minimum this project will determine how competent state governments are at managing the voter rolls when people move out of state and register with another state.

From personal experience my child moved to another state last spring (2016), registered to vote there and is STILL on the voter rolls in Colorado today.