We generally wish to to reassure a person who is scared ("everything will be fine"), even without anything to base ourselves on. A way to avoid the problem, to believe we can "save" someone, or to reassure ourselves. However, this rarely works because fear, even at its most irrational, is always justified to the person it inhabits. To reassure someone immediately is to downplay the significance of what they feel and to show that we don't really hear them.       

The most important thing is to allow your co-worker to say clearly what he is afraid of, and for him to be heard. What does he fear the most? Why? What information does he have? What does he think about it? Are there other possible versions? …
For it is when we make a subject taboo or we avoid it that its potential to do harm grows.       

The most reassuring thing for a co-worker: to be able to have confidence in his manager as both a person and as a representative of the enterprise! To know that he is transparent and forthright in his relations. This means sharing your own vision of the situation while distinguishing what is helpful from what isn't, communicating your convictions or those of the company, underlining your commitment, etc.
The questions to ask yourself are then: what is the principal message that this co-worker is trying to express, to me? How to show him that I have understood? What message should I offer him in return?