Like ChrisMwn said, INZ is like any other office and staff come and go and get moved around all the time, so yes, there are many people who have had their case taken on by someone else in the middle of processing. All officials keep notes of what they do on a case as they do it, so the new person just takes up from where the first one had got to.
You may find that things do not move very fast on your application. When, as is your husband's case, someone is already on a visa in NZ, legally working, they have a low priority. It's as if INZ think there's no hurry for such people, when there are others who need their first visa put in place so they can start earning. I know this takes no account of your natural wish to have everything sorted out. If he gets to eight weeks before his work visa expires, it's fair enough to point this out to INZ, and things would move very quickly at that point. Here's hoping it doesn't get that far, though.