When a person dies, the funds in their health savings account are transferred to the beneficiary named for the account. If the beneficiary is a surviving spouse, the transfer is tax-free. If the beneficiary is not a spouse, the account stops being an health savings account, and the fair market value of the health savings account (less any unreimbursed qualified medical expenses of the decedent paid within the 1 year anniversary of his death) becomes taxable to the beneficiary in the year in which the health savings account owner dies.