As was said, if their names are both on the mortgage, they are equally responsible for the debt. Likewise I assume that they are also joint owners.
I can only assume that he does not have the income to qualify for the mortgage on his own. If he does want to keep the house then he will need to either find another person to share ownership or of course find another source of income to qualify by himself. Perhaps he could consider renting a portion, although I am not sure of the current rules regarding rental income used as qualifying income.
There would certainly be some legal costs involved.
Depending on when they bought and their downpayment they may also be in a negative equity situation?
If they can get out and remain whole I would think that selling the property and discharging the mortgage would be the smartest thing.