If bank will put house in ex's name, or there's any other way your friend can get name removed, they should go for it.
In fact, she should be happy to give him half the negative equity to walk away from it cleanly, so tell her to get the cheque book out.
Are they actually divorced, it separated? If divorced, was there any agreement in relation to this property? If not, then why?
Your friend needs legal advice in that scenario. There are many different circumstances so you won't get advice without the full facts, including reviewing the title documents.
From what I am reading, the wife seems to be concerned about the husband making money on the property in the future. What she is neglecting to look at is that he is taking on more debt than the house is actually worth, a debt he is relieving her of. As RedOnion said, is she going to write a cheque to her ex husband for taking on all the debt?
He could pay rent himself. So the half payable to him goes to the bank as a mortgage repayment, with no income tax liability to himself. The other half is paid to the ex wife as rent. She forwards it on to the bank to cover her half of the mortgage. She has to declare it as income and pay tax on it.
She will also still be liable to the full value of the debt on the property and be unable to get another mortgage herself so she can move on.
The current arrangement of him paying the mortgage is cheaper for her and him taking her off the mortgage means she can move on.
From a financial point of view, I can't see why she would hold on (from an emotional point of view, there are many!)
Edit: There is also a risk that he may be worse off in the future too, especially if he is effectively buying the house at a higher price than it is worth. If she wants a share of future gains, she will also have to share of future losses. Is she willing to do this?