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My friend has gone through the same situation. It seems that he was in still worse a situation, as he had run out of the six-year limit of H1-B visa. As had been told to me by him, I shall give below the way he is manoeuvring the situation:
He received the EAD card just after the lay-off. Based on the EAD, he found another job, but the new employer would not take him as an employee there, because he was told that the EAD is not transferrable. So, he got the job contracted to his previous company: the new company would pay the old company. The old company reinstated him and he continues to receive his salary.