The Fairfax County Board of Supervisors has fixed a loophole in its tax code that would have caused affordable housing nonprofit organizations to lose property tax exemptions on their properties, even if those properties were transferred to other affordable housing organizations or simply refinanced.

At its regular meeting Tuesday, the board voted unanimously to tweak the code to protect the tax exemption for charitable housing groups such as Fellowship Square Foundation, which provides dwellings for elderly people and people with disabilities, and NOVACO, which provides housing for people who must leave their homes because of domestic violence.

John Thillman, a director of Fellowship Square Foundation, said the tax exemptions help the organization provide assistance to low-income people whose monthly rent and medical expenses are more than their annual income.

“These people are desperate,” Thillman said.

Without a change in the law, for example, the tax exemption would disappear on five townhouse condominiums operated by Lutheran Social Services as affordable housing if the charitable organization conveyed them to NOVACO for the same purpose, county staff said.

Recent attention to the loophole in the code has renewed discussion about whether Fairfax should consider offering tax exemptions to nonprofits that offer other social services too.