With the second-oldest population in the country, Vermont needs its nursing homes. Yet, while Vermonters rapidly age, the state’s long-term care capacity has dwindled, losing 900 beds in the last two decades. To keep the struggling system afloat, the state has bailed out nursing homes with around $38 million in state and federal Medicaid dollars for what are known as extraordinary financial relief over the past five years, according to records obtained by VTDigger.