If the spouse is on the mortgage, he/she remains in privity of the contract between the bank and him/herself unrelated to his/her spouse. The reality is that if one party is solely on the mortgage, that person is required to pay it in full.
If, for example, the husband is jointly liable for the mortgage and fails to pay it, the mortgage holder is going to look to both spouses to pay, and my recommendation is that the wife has no choice: She should file for divorce and get a temporary order obligating him, through the court system, to pay his percentage of the mortgage, as the court sees fit.