This is a totally natural physiological and psychological response to threat. Your job is often a part of your core identity, and to be separated from it threatens your sense of self. And the worry of not knowing who, what, where, and when stimulates the fight, flight, or freeze responses. Completely natural and nothing to be ashamed of!
We have to remember that we are NOT our jobs; our jobs are an extension of who we are. Those who know for sure that they've been cut or been given the all clear are the blessed. For separated employees, you're going to bring your "self" and all your talents to a new setting, and I can guarantee it will be for the better!