My company cut my pay in HALF, and want me to resign, Does GA law allow me to get unemployment?

I live in CA. I was laid off in April and got several weeks of unemployment before finding a job. I was offered a regular employee position, but never got on payroll. The have been paying me via the equivalent of expense checks, they pay no tax, nor do they take out any for me. They just cut my pay in half (which is less than my unemployment benefits had been), and said if I didn't like it I should quit (they refuse to lay me off or fire me). What is GA law on this? Can this be constructive termination? They're no longer paing me what they agreed to in their offer letter, but don't want me getting unemployment because it will have repurcussions to them, as CA doesn't know they exist.