Laid off - if company offers me a job again and I refuse do I lose unemployment?

I was laid off about a month and a half ago (in a massive layoff at my company) and now there is a different position open that it looks like they will offer me. But the company is falling apart and I don't want to work for a company that both laid me off and is not doing well. But if I turn that down, do I lose qualification for my unemployment?