Whenever any person claiming the exemption from property tax under the provisions of subdivision (59), (60), (70), (72), (74) or (76) of section 12-81 has failed to file a claim with the assessor or board of assessors as required in said subdivisions and has further failed to apply for an extension of time under section 12-81k, the municipality, upon receipt of a request from such person, may, by vote of its legislative body or, where the legislative body is a town meeting, by a vote of its board of selectmen, grant such exemption according to criteria established by the municipality, including, but not limited to, allowing for any hardship experienced by the person which may account for the failure to claim the exemption or to file for an extension of time and whether the exemption would provide a net benefit to economic development in the municipality. No payment in lieu of tax under this chapter shall be made with regard to any property exempted from tax under this section.