Any mortgage or lien against the property stays with the property regardless of whose name is on the title. So, the house will continue to be considered collateral for the debt even if he removes his name from the title. Because laws vary by state, your mother-in-law would be wise to consult with a qualified attorney to determine her best options moving forward.
Generally speaking, a lien is satisfied only when it is paid or released by the person or entity that placed it. Since the reason for the lien was child support, it's possible that it was requested by your state's Office of Child Support Enforcement. If that's the case, your mother-in-law should consider contacting the agency to help it collect what's owed.
States have the power under the Title IV-D of the Social Security Act of 1975 (Child Support and Establishment of Paternity) to garnish wages, intercept tax refunds, unemployment benefits or workers' compensation, seize and sell personal property, suspend certain professional licenses and passports, and in some cases, pursue criminal charges. Should the state be willing to pursue any of those remedies, the lien against your mother-in-law's home would be satisfied and could be removed.
Your mother-in-law also should consider how much equity she has in her home. The lien placed on the home for back child support would be paid after the mortgage loan was satisfied when selling the home or refinancing the mortgage. Bankrate, by the way, has tools that can help her decide whether to refinance the mortgage.
If there is not enough equity to pay the child support lien at the time of sale, it would still be owed by her ex-husband, but the home would no longer be the collateral. In most cases, however, it is difficult to sell or refinance with a lien on the home.