Can my unemployment benefits be taken away?

I have been working for my company for 1 year now full time. Because of the economy they have reduced my hours to a part time position. At the current moment there is an opening for more hours. And would like to apply for the position, but the position is more physically demanding than the one I currently have, and would be harder for me to do since I have carpotunnel. Would my unemployment benefits be taken away if I don't interview for the position? or if I reject their offer? how would it be if I didn't have the disability?