You can only apply for a Declaration of Law when you have found a job in Curaçao. So it is not the case that you first need a work permit or Declaration of Law before you can start working. The government wants to be sure that you will earn money when they allow you to work.

So you are in the process of applying for a job and the employer asks for your Declaration of Law? That is not possible because you must first have an employment contract before the application can be submitted.

It is true that as a Dutch or American citizen you are allowed to start working while you are awaiting the Declaration of Legal Status.