New Zealand husband died suddenly, can the wife apply for immigration to New Zealand?

You can't. According to the information in 5 1.com, you can apply for a spouse work visa after you have been married or cohabited with a New Zealand resident or citizen for 12 months. For couples who have just married or lived together for a short time, the approval time will be as long as 6 to 12 months to examine the authenticity and stability of the relationship between husband and wife. If you don't have enough time to get married or live together, or if you don't have enough time for approval, your wife can't apply for immigration to New Zealand.