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Federal and state income tax liabilities are calculated separately - that is true for individuals for corporation and for estates.
So - there is no double dipping.
If there are deductible expenses for federal income tax purposes and the estate does not file the federal income tax return (form 1041) - these deductions are "lost"
If the administrator of the estate chooses to file the estate tax return (even otherwise it is not required) - and if that is a final tax return for the estate - unused deductions are passed to beneficiaries - and may be used on their individual tax returns.