New Jersey will probably consider prosecuting former state residents for tax evasion.
After all, they probably moved to escape the state's confiscatory taxes, which proves motive.
New Jersey won't have the authority to do that. However, I can certainly see the state imposing something similar to California's rules for state government retirees in the state's own pension system . . . i.e., where pensioners in the state system must pay state income taxes in New Jersey regardless of where they live after retirement.
Even with a measure like this in place, there's a decent chance New Jersey will be the first state in the U.S. whose pension fund goes bankrupt.