The Verdict: Unlikely
As a stateless person you can ask the Minister for a grant of citizenship outside the usual rules, but it is discretionary. Gather written evidence that no country recognises you, and take advice before applying.
Section 9 of the Citizenship Act lets the Minister grant citizenship where the applicant would otherwise be stateless, without having to apply the five years or the day counts. It permits a grant; it does not require one, and we found no published criteria. That is why we rate it a long shot rather than a likely result.
Stateless means no country recognises you as its citizen under its own law. Being unable to get a passport or reach a consulate is not the same thing.
Your immigration status in New Zealand still matters in practice. A refugee and statelessness service or an immigration lawyer can help you assemble evidence from each country with a claim on you.