Thanks for filling in the details. It seems like strong emotions are a trigger for him to that earlier, unhappy time in his life. When his wife shows emotions, it may bring him immediately back in his mind to his ex. He has a degree of trauma, and when similar things trigger the trauma response, he may be getting flooded with fear and sadness, even if the present situation is nowhere near as bad as with his ex. His brain will automatically react as if he is back in the past. Because that time was so incredibly painful for him, in order to not feel all of it again, his only choice is to shut down.
This is not a reaction that he can control. His wife may need to vent her emotions with friends and try to interact with him when she can be more in control of her emotions. This is a tall order, but he really can't help his reaction--it's not something he chooses, but is an automatic reaction due to trauma.
The other way to help a person who is being triggered is to help him stay grounded in the present. She may find that expressing her emotions while they walk together (the walking will help keep him in the present, because he has to stay aware of his body) or while they work side by side on an activity or chore will get her more empathy from him. People who have had trauma can "check out" mentally when triggered--moving the body is the easiest way to keep them in the present.
The fact that he would like to express and tolerate more emotion shows his reactions aren't due to a lack of caring. If your friend can learn to accept that his shutting down is like an old injury, and not take it personally, taking some of the pressure off him to respond emotionally may improve their relationship. It's a tall order, but if she can realize that he's there for her on a day to day basis, and just shuts down due to this 'old injury' maybe she can realize that he's showing her his love the best he can.
Of course, if his financial situation improves, it would be wonderful for him to have some therapy to heal those old wounds and enable him to be more fully emotionally present with his current wife.