The State Department released a statement by Mrs. Clinton, who worked from home after a bad fall late Wednesday in which she fractured an elbow. She is expected to have surgery within days, spokesman P.J. Crowley said. Thursday’s order marks a significant change in policy, and officials said it goes into effect immediately. The State Department will now cover the moving expenses of domestic partners of gay Foreign Service members on their way to a new assignment, as well as the cost of any emergency evacuation.