WEST PALM BEACH, Fla. — With almost one in five residents in Palm Beach County lacking health insurance, officials here thought they had hit on a smart solution. The county launched a program that offered subsidized coverage to residents who could not afford private insurance but who made too much to qualify for Medicaid, the state-federal program for the poor. Enrollees would be able to buy policies for about $52 a month — far cheaper than what private insurers were offering. But a year after the program began, fewer than 500 people had signed up — less than a third of the number expected.