A resident can work for any employer.
Otherwise, there are very few situations where anyone can get an open work visa - the one most frequently encountered is a partner-sponsored temporary work visa, where a person has a live-in relationship with someone else who has a work visa, NZ residence, or NZ citizenship, in which case they can work anywhere, but the visa is dependent on the continuing relationship, and in the case of living with a work visa holder, their visa will only last as long as his/hers.