CalGreenCard
Registered Users (C)
Actually, a GC would only be awarded to for a permanent position (employee) of a firm, never to a contractor. Once you have a GC, and as long as you and the employer/sponsor are fulfilled the terms of your GC sponsorship for the requisite time, you can do (or not do) what you wish, including being a contractor.
But GC-sponsorship is employment-based, if that is clearer.
A self sponsored EB1 GC can be awarded to a contractor.