Permanent Residency with the Right to Work
Almost all persons who reach eight years of continuous legal ordinary residence in the Cayman Islands are eligible to apply for Permanent Residence with the Right to Work.
Permanent Residents will have to continue paying CI$500 per year per dependant until they (or the Permanent Resident) becomes Caymanian. If you are on a government contract, and receive PR, you appear to have the choice of putting your dependant children on your PR (and paying the CI$500 fee per year) or keeping them on your government contract and paying no fees for them. There are other rules worth considering.
The spouse of a Caymanian has no inherent right to live or work in the Cayman Islands (apart from any unexpired permission they may have held before being married to a Caymanian) unless they apply for and have granted a Residency and Employment Rights Certificate as the Spouse of a Caymanian.
The surviving or former spouse of a Permanent Resident is required to notify the Director of WORC and the Caymanian Status & Permanent Residency Board of their change in circumstances within six months. Within these six months the surviving spouse, or former spouse, may be eligible to apply for the grant of a Residency & Employment Rights Certificate in their own right. It may be important to consult with a lawyer or reputable immigration services company to confirm your standing and options in the event of appropriate circumstances arising.