Hello Kiwij and welcome to the forum.
Can I ask what type of visa does this lady have? If she has Permanent Residence then I don't think she has to stay with this man. She should have her own visa stamped in her own passport, so that, if she ever wants to travel outside NZ, she can do it on her own. The only way she could be tied to this man is if he was the owner of a company she worked for and she had a Work Permit linked to the company. Nevertheless, if this was the case, she could find another job and have the conditions of her WP altered to the new company. It should be said that, if there is a current application for her residency going through at the moment, the man could stop it if he is sponsoring her. He could withdraw the application if she left him.
I can't see that it's correct that she should have to stay with him unless he's made some complicated arrangements with her visa so that she has to stay, but I can't imagine what. It sounds like this story is something the guy has made up to try to frighten the lady into staying with him. She needs to get her passport and check if there is a blue sticker in there which would be her residency permit. In fact I believe there should be 2 blue stickers in there, one for residency and a returning resident's visa for when she needs to leave and re-enter NZ. If she does have PR that means she can stay in NZ with or without this man and he shouldn't be able to do anything about it if she wants to leave him.