My company is being sold. We are considered terminated with transfer. Should I sign?

We will all receive a contract offering employment with the new company. I don't want to sign it, but they say if I don't I will be considered voluntarily resigning (if I resign I have to pay back some $$). Can they just say that I resigned, if I didn't? I am not leaving the company, they are leaving me.

It sounds very fishy to me. Before they can hire you, they have to terminate your positon. In which case you are eligible to file for unemployment.
This whole thing about you resigning unless you sign something sounds like B.S.
You don't resign from a job unless you explicity state that you quit. Sounds like they might be trying to weasel out of paying their part of unemployment compensation. I think you should talk to the labor deparment, and or a lawyer before signing anything.

I would say that the company you work for has sold everything. Including the contracts with employees. It depends on what is stated in your contract (in the really small print) whether or not this is considered a resignation because of the circumstances.
You never know this could end up being a good thing for you. Your staying on with the new company might show them something they like about your character. And they may offer you more money, benefits, etc. I would check into meeting with the new management and seeing what their plans are. Seems to me that they like the way the company is being ran and want to keep it that way. Change is not always such a bad thing. Hope this all works out for you.