What to do regarding payment of franchise tax on a non-operational corporation?

Question Details: My father was a retired inventor, who was hopeful that he would invent a marketable product. He is now deceased. About 35 years ago, he registered a corporation in DE. The corporation never had any assets, liabilities or stock issuance. It has not conducted any business of any kind since its registration. With the passing of my father, there are no other officers in the corporation. DE is requiring fees to be paid for the annual franchise tax, a late tax penalty with applied interest of 1.5 per month, and fees to dissolve the corporation. My mother has severe dementia and lives on social security. Who is responsible for paying the company's obligations?

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