If they fire you as an individual and then bring you back, certainly. If it's part of a layoff done this rapidly, its much more likely that it was just a categorizing error. So you probably don't have massive leverage.

That said, you definitely shouldn't accept a worse deal.

Yeah, I’ve had this happen, and I demanded twice my salary.

It was a contract position, so you can’t be “let go.”

A fool, or someone without many options.