(6) A rent exemption order shall be valid for the period of the lease or renewal thereof upon application by the tenant; provided, that upon any such renewal application being made by the tenant, any rent exemption order then in effect with respect to such tenant shall be deemed renewed until such time as the department of finance or such agency as the mayor shall designate shall have found such tenant to be either eligible or ineligible for a rent exemption order but in no event for more than six additional months. If such tenant is found eligible, the order shall be deemed to have taken effect upon expiration of the exemption. In the event that any such tenant shall, subsequent to any such automatic renewal, not be granted a rent exemption order, such tenant shall be liable to the owner for the difference between the amounts the tenant has paid under the provisions of the automatically renewed order and the amounts which the tenant would have been required to pay in the absence of such order. Any rent exemption order issued pursuant to this subdivision shall include provisions giving notice as to the contents of this paragraph relating to automatic renewals of rent exemption orders and shall include provisions giving notice that the tenant must enter into either a one or two year renewal lease in order to be eligible for a rent exemption. The notice that each tenant receives from the owner relating to the right to a renewal lease shall contain similar information. Any application or renewal application for a rent exemption order shall also constitute an application for a tax abatement under such section. The department of finance and such other agency as the mayor shall designate may, with respect to renewal applications by the tenants who have been found eligible