Also, it's worth keeping in mind that the default Section 49(1) conditions applied to the Skilled Migrant Category actually don't restrict you to a specific employer -- but they do mean that one has to be careful if taking up new employment that such new employment meets the same criteria as the old employment for the grant of SMC points.
If one looks at the conditions that may be applied (over in
SM11.5 of the ops manual), and look at what I personally view as the most restrictive condition (applied if the principal applicant is not currently in skilled employment but has an offer of skilled employment outside of Auckland, which is condition (c) in SM11.5), the wording is as follows:
(i) The principal applicant must take up that offer of skilled employment within three months of their first entry to New Zealand as a resident (if the visa was granted outside New Zealand), or the grant of their resident visa (if the visa was granted in New Zealand); and
(ii) The principal applicant must remain in that employment (or another position of employment that meets the requirements for current skilled employment including requirements for bonus points if the employment qualified for bonus points under SM6.40 or SM6.50), for a period of at least 12 months.
The rest of the conditions that may be applied have the same sort of wording, the difference being that part (i) is not applied if the principal applicant is already in skilled employment, and part (ii) is only applied for 3 months if no bonus points for employment outside of Auckland are claimed.
The key wording is: "... or another position of employment that meets the requirements for current skilled employment including requirements for bonus points if the employment qualified for bonus points...". If the Section 49(1) conditions contain that wording, then the principal applicant can resign, but the new position must meet the same requirements for skilled employment as the old. Particularly, there's another condition that will be applied stating: "The principal applicant must be remunerated for the employment at or above the level of remuneration [...] on the basis of which points for skilled employment were awarded, for the duration for which any conditions are imposed..." (this can also be found in SM11.5), so if the new position pays less than the old one, one can expect to run into difficulty later.
Realistically, I would guess that most people would prefer to just stick it out with their current employer until the Section 49(1) conditions are met and removed, just to avoid any potential hassle if INZ does not recognize the new employment as meeting the requirements for "current skilled employment" and/or if the new employment pays less than the old. Certainly, that's what I would aim to do if I were in that position -- in my experience, it pays to have a cautious approach when dealing with INZ.