CHARLESTON, S.C.—Housing Secretary Ben Carson says his latest proposal to raise rents would mean a path toward self-sufficiency for millions of low-income households across the United States by pushing more people to find work. For Ebony Morris and her four small children, it could mean homelessness. Morris lives in Charleston, South Carolina, where most households receiving federal housing assistance would see their rent go up an average 26 percent, according to an analysis done by Center on Budget and Policy Priorities and provided exclusively to The Associated Press. But her increase would be nearly double that. Overall, the analysis shows that in the nation’s 100 largest metropolitan areas, low-income tenants — many of whom have jobs — would have to pay roughly 20 percent more each year for rent under the plan.