Like with most issues there is no one answer. Then put in place some plans to answer these issues. For a start, developing an open relationship with high-risk staff is critical. By the way, the old story if they are Indo Fijian they'll migrate if not they won't is long gone. Okay some will lie but if you have recruited well most will be honest as long as they trust you and know that you wont penalize for being honest.
Fraud is sometimes a reason for their subterfuge.
Personal and honest counseling sessions can really help. Being able to sit down with them openly and honestly discuss their options could head off migration plans, particularly, where they are about to sacrifice a good career to become an Auckland taxi driver. Once you are aware of your risk, set up a plan to keep key staff or if they are going, planning their replacement. This means increased training and development work, it could also mean increased efforts at providing growth opportunities for key team members by adjusting job descriptions. It also could mean increased capital expenditure.