After your last day of work, appy for unemployment benefits. NOW. You don't even need to mention that this new company has offered you this job.
One of the questions you will eventually be asked (probably on your first week's certifications) is if you have been offered, refused, etc. any jobs this week for which you are certifying.
This deal they have presented to you is not a real job offer. Don't worry about not returning the information. No wise person would agree to sign up for a blind calf like this. This is not a legitimate job offer. This is the new business trying to discourage people from filing for benefits, in hopes they'll just march right over and come to work for them.
But no one has the right to keep you from filing for unemployment benefits, your job has closed and you no longer work for xyz company through no fault of your own, and once you have filed a claim, and given them all the information they ask for to file the claim, which does not include telling them about this letter business, there's not a lot of danger that this much of a job offer will be considered refusal of a legitimate equivalent job.
You simply do not have enough information to determine if it is a suitable job for you right now, they didn't provide you with that, and neither does the unemployment office. You file your claim, you state that you are able and available and actively seeking equivalent work, and then later, if you are contacted by the unemployment office about this so called "job refusal" which they may do, as the new company may turn in a list of names of people who turned down this great deal they offered. You may be called about it, but you just tell them at the unemployment system exactly what is the truth, you were asked to agree to accept a job with a new company when you knew nothing and were given no details at all about the new job being offered to you.
