I noticed the article in the WSJ about New Zealand. But I (a kiwi) haven't seen any local news indicating that the government has declared any sort of elimination. If you have seen one, could you link it? I'm currently skeptical of the WSJ article.

There were four new cases today. One confirmed by test and three presumptive cases which according to the experts probably have it. Plus there are hundreds of people in isolation/quarantine who are still sick. I wouldn't declare "elimination" just yet.

Even if new cases dwindled down to zero, that doesn't imply elimination either. There might be many asymptomatic people who are not spreading it currently because of the lockdown, but who will start spreading it once they start interacting with people outside of their bubble.