Hello so so sad
Welcome to the forum and thank you for your thread. It is difficult when our children are hurting and we realise we cannot "kiss it better" as we did when they were young. I am sorry your son lost his job in that way. It seems pretty harsh for one mistake and more so with the effect it has had on his mental health. Unfortunately it is easier for organisations to simply tell a volunteer not to come again. If he was a paid employee the company would need to justify their dismissal.
Is there any way you can speak to his manager and ask them to reconsider?
Encouraging your son to talk about his hurt and disappointment may not seem much but it is a great reassurance that he is loved, even though you do not say so. Sometimes the person can feel cut off from everything and would welcome this encouragement.
May I ask, does your son have a therapist? If not maybe it would be a good idea. It would be another person to offer support and perhaps some offer ways of coping. You know your son best. Do you know any ways of helping him? Perhaps something that has helped in the past.
Is your son looking for another volunteer role? This may give him a sense of purpose though he may not be ready for this just yet. It is always hard finding a new job no matter how skilled the worker is. What does your son enjoy doing? It may be useful to tap into something he feels enthusiastic about.
I'm sorry I cannot give you more specific suggestions. Please continue to post here.