HSA funds are owned by the deceased, and now the estate of the deceased or a beneficiary. If the beneficiary is a spouse, they may continue using the account. If the funds go to a non-spouse beneficiary it will be taxable income to the beneficiary. And if the funds go to the estate, special tax rules apply but essentially it's income to be shown on the decedent's final tax return. The authorized signers rights ended when the owner passed.