Legal Question in Employment Law in Illinois

The company offered you a position. You had to accept in 3 days. You accepted late. The company didn't withdraw the offer but allowed you (apparently) to start the new position. The company therefore waived its right to withdraw the offer. That's a done deal. They can terminate you now for failure to perform the new position, and what happened before is irrelevant. However, if there's more to this situation, such as that the company knew you couldn't handle the new position and was just setting you up to be fired, the answer may be much different. What is also unclear is why they felt they needed to make a formal offer to you? If you have a collective bargaining agreement, other work contract, or workplace rules that require this kind of offer, then you may have additional rights. Otherwise they could have fired you (or you could have quit) without having made any offer....as Illinois is an "at will" state (you can quit/they can fire at any time for any or no reason if there are no such workplace contracts....).