A mailing glitch by a Massachusetts agency left 16,000 residents without proper notice that they might be losing their healthcare coverage or information on how to appeal a denial of coverage. The notices were mailed about a month after they should have been sent. In the meantime, some residents may have lacked health insurance, potentially leaving them at risk for enormous out-of-pocket medical bills. MassHealth, the state Medicaid provider, said it would cover medical bills for any resident that was left without coverage as a result.