Harold Labrensz spent much of his 89-year life farming and ranching the rolling Dakota plains along the Missouri River. His family figured he would die there, too. But late last year, the nursing home in Mobridge, S.D., that cared for Mr. Labrensz announced that it was shutting down after a rocky history of corporate buyouts, unpaid bills and financial ruin. It had become one of the many nursing homes across the country that have gone out of business in recent years as beds go empty, money troubles mount and more Americans seek to age in their own homes.For Mr. Labrensz, though, the closure amounted to an eviction order from his hometown. His wife, Ramona, said she could not find any nursing home nearby to take him, and she could not help him if he took a fall at home. So one morning in late January, as a snowstorm whited out the prairie, Mr. Labrensz was loaded into the back of a small bus and sent off on a 220-mile road trip to a nursing home in North Dakota.