In New Zealand an employee is usually contractually required to give notice, and there is a default of “fair and reasonable” notice. However I would guess it is very unusual for an employee to be significantly penalised if they do not work their notice period. Even though an employer may legally be able to seek damages (not exceeding employee replacement costs), that doesn’t look common to me. Employment in New Zealand is mostly a moral, reputation, and trust based system.
A company cannot withhold an employees pay or holiday pay. An employee contract can override that default so that a company can withhold pay. However the employee can override the contract by simply writing a letter to the employer.
https://www.findlaw.co.nz/articles/4336/what-happens-if-i-do... https://communitytoolkit.org.nz/staff-and-volunteers/termina...
Disclaimer: I have no special knowledge of this area, it is just a summary from a quick googling.