No: debt is not inherited.
One caveat: while debt is not personally inherited, liens, mortgages, or security interest on property has to be paid off or else the property cannot be inherited free and clear--the lien stays with the property after the owner dies. So if the IRS has put or does put a lien on any of your property (e.g. real estate), if your heirs want to inherit it, they'd have to choose to pay off the lien...but are free to not take the property if they choose, and if they don't take title or care about the property, they would have no obligation vis-a-vis the lien.
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