It is really disappointing from management end to convey this kind of message in this manner.. I think you should check with management the reason for your layoff with the company. Secondly if they are giving you full month salary & employer mentioned you that you're not terminated it is good for you. Because I guess they don't have proper evidence to terminate you.
You can ask them reason and also check them if they will give you relieving letter or not. You have one month time to get into other job. There's no use of wasting time to convince them to take you back. Try to get relieving letter & another job.
Please take care when you are sharing reference details of your present employer to future company.
From India, Pune
From India, Salem