Actually, in OK, there is very little possibility of receiving partial unemployment benefits while working as a temp, because the weekly benefit for unemployment, maximum is probably still going to be less than you would possibly be able to make in gross wages for a week.
I would advise you to go through the termination procedure, and set up your unemployment claim immediately as soon as you have your last official day of work. DO NOT sign anything or agree to accept anything in regards to the temporary employment position while dealing with your old company. You are being laid off from your old company. You will no longer be working for them, whether or not you do decide to accept the temp assignment.
Do not let the old company tell you they can cut off or not agree for you to have unemployment if you do not agree to work for the temporary service. You are being taken off their payroll, placed in lay off status. You are unemployed through no fault of your own, with or without severance. File for benefits right away.They have no control over whether the unemployment system approves or denies your unemployment claim.
You are required to be able and available for equivalent work (which in the beginning will probably be work that has equivalent or nearly equivalent pay, and probably work that provides benefits) But whether or not you register with the temp service for your old job without benefits or as good a pay or job security of any kind (being a temp job) is your decision. Of course, if the temporary service were to call you up and demand you register with them and offer you the job, there would be the necessity for you to report to the unemployment office that you were offered a job.
But your old employer cannot offer you or force you to take a job with the temporary service. The temporary service is the employer who would have to offer you the job and you'd have to refuse it, and even then, if you had not been unemployed very long, there would be a very iffy situation as to whether it would be considered an offer of equivalent work sufficient to stop your unemployment claim.
Now, all that said, there's still a very good argument to be made for actually going down and registering and accepting your old job back in a very abbreviated form, unless you sincerely believe that there will be better jobs out there for you to get. Because unemployment insurance does not pay very well at all, and it ends abruptly when it ends, whether you have found a job or not. In other words, you don't want to be looking at nine months from now, you wish desperately you had accepted the temp job and you didn't and now you have nothing at all.
I would know that your former employers are creeps who are playing on the desperate work force to accept their restructuring. But I've seen employers do as bad or worse, shutting down and getting rid of the "blue hairs" so they can reopen with younger, more poorly paid employees (if they even stayed in the country at all. It's legal for them to do it. I would do my utmost to find another job somewhere else as soon as possible.
Now, all that said,
Whether or not you accept the same job, with no benefits, a much smaller salary you cannot be transferred by your company to a temp position. You are going to have to be offered the position, and accept it, as a temporary worker, at a lesser salary, with no benefits. Up to you to decide whether you want to do it, or go for something else with another company soon.