What happens to a rural town after it loses its only school? Arena, Wis., is about to find out. Arena Elementary is the second small rural elementary school in two years to close in the district, nearly 300 square miles of rolling pastures and dairy farms in southwestern Wisconsin. The one in the neighboring village of Lone Rock closed last spring. The district now has just one open public elementary school, in Spring Green, nine miles away.The same scene is playing out across rural America. Officials in aging communities with stretched budgets are closing small schools and busing children to larger towns. People worry about losing not just their schools but their town’s future — that the closing will prompt the remaining residents and businesses to drift away and leave the place a ghost town. Rural schools have been closing in waves for decades, but the debate has taken on sharp urgency this year, particularly in communities in the Midwest and New England that have grown smaller and older since the recession. In Wisconsin, Gov. Scott Walker, who is under pressure as he campaigns for a third term, signed a bill in March increasing aid to nearly 150 sparsely populated school districts. A legislative committee in Madison, noting the major shifts in population from rural areas to cities and suburbs in the last decade, has convened public sessions across the state to search for solutions and hear from frustrated parents and administrators.