A growing number of cost-controlled homes in Fairfax County that had been set aside as affordable housing are facing foreclosure, county officials said Monday, prompting supervisors to examine how to halt the loss of the in-demand units.

The homes, mostly town houses, are part of the county’s “affordable dwelling unit” program in which developers set aside a certain number of properties for low- and middle-income families at below-market rate, in exchange for permission to build larger developments.