Can I reopen an unemployment claim after doing contract work?

I was laid off in April. I opened an unemployment claim, within weeks accepted a sales job at a firm HQ in GA. While is was to be a regular employee position, they have only paid me via straight check, no taxes paid by them or for me. Now they informed me due to the state of the business they are cutting my salary in HALF, and that is even less than what my unemployment benefits would still be today if I didn't take this job. I never would have taken it knowing this. I know they want me to leave as they are evolving into a "service" company, and I sell new business. However, they will not lay me off or fire me, they said I can "resign". But will I be eligible for benefits if I do resign under this pressure?