(b) If any portion of such real property of such corporation is not used exclusively for housing of those persons set forth in paragraph a of this section but is leased or otherwise used for purposes pursuant to article two of the private housing finance law, such portion, provided it does not exceed ten per centum of the total, shall be subject to such limited exemption as is authorized pursuant to article two of the private housing finance law, and the remaining portion only shall be fully exempt. If any portion of the real property of such corporation in excess of ten per centum of the total is leased or otherwise used for housing pursuant to article two of the private housing finance law, the total property shall be subject to such limited exemption as is authorized pursuant to article two of the private housing finance law. Real property exempt from taxation pursuant to this paragraph shall also be exempt from special ad valorem levies and special assessments to the extent provided in section four hundred ninety of this chapter.

(c) In real property used in part for handicapped or aged persons of low income priority and preference in the rental of such real property for purposes not specified in paragraph a shall be given to a family of a person legally responsible for the care of a handicapped or an aged person residing in such real property. This preference and priority shall apply to only one such family for each handicapped or aged tenant. 2. (a) The exemption provided in paragraphs (a) and (b) of subdivision one of this section shall be upon condition that the property owned by such corporation shall upon dissolution vest in such college, university, educational institution, hospital, medical research institute, child care institution, or other not-for-profit corporation, if such college, university, educational institution, hospital, medical research institution, child care institution, or other not-for-profit corporation is exempt from taxation pursuant to the provisions of section four hundred twenty-a or four hundred twenty-b of this article and if no part of the net earnings of such college, university, educational institution, hospital, medical research institute, child care institution, or other not-for-profit corporation shall inure to the benefit of any private individual.

(b) In the event that such college, university, educational institution, hospital, medical research institute, child care institution, or other not-for-profit corporation is not otherwise exempt from taxation, title to the property shall nevertheless vest therein, but only upon payment to the municipality of a sum equal to the total of all accrued taxes, levies and assessments from which such property has been exempt under the provisions of this section.