If it is a permanent resident visa without conditions, your visa should not be cancelled even if your nationality changed and your passport is cancelled. But you will need to apply for a transfer of eVisa with details of your new, valid US passport.
https://www.immigration.govt.nz/new-zealand-visas/already-have-a-visa/transferring-my-visa-to-a-new-passport
64 Cancellation of visa on triggering event
(1) A visa is cancelled in the following circumstances:
- (a) on the deportation of its holder from New Zealand:
- (ab) on the day after the first date on which a deportation order may be served on the person under section 175A, whether the visa was
issued before or after this paragraph came into force:
- (b) on the refusal of entry permission to its holder:
- (c) on entry permission granted to its holder being revoked:
- (d) if the holder arrived at an immigration control area,— (i) on the holder leaving the immigration control area without presenting
himself or herself to an immigration officer; or (ii) on the holder
failing to comply with the instruction of an immigration officer to
remain in the area:
- (e) if the holder arrived at a place other than an immigration control area, on failing to present himself or herself in the
prescribed manner and within the prescribed time as required under
section 103(1)(b):
- (f) on the start date of a further visa granted to its holder:
- (g) on the grant of New Zealand citizenship to its holder:
- (h) on the registration of New Zealand citizenship by descent under section 7(2) of the Citizenship Act 1977 by its holder:
- (i) on the issue of an evidentiary certificate under section 21 of the Citizenship Act 1977 that confirms the holder is a New Zealand
citizen.
http://legislation.govt.nz/act/public/2009/0051/latest/whole.html
A change of nationality does not create a deportation liability (fraud, forgery, character, crimes, security etc.) nor form any ground to refuse entry permission (provided the visa is transferred).