Fairness In Failed Federal Exchange Act of 2013 - Amends the Patient Protection and Affordable Care Act to deem an individual not covered by minimum essential coverage and who is eligible to enroll through a health care exchange under a qualified health plan: (1) for a month in 2014, to have had a certification by the Secretary of Health and Human Services (HHS) exempting the individual from the individual mandate and the associated penalty on the basis of the hardship exemption; and (2) for a month in a subsequent year to have had a certification of hardship exemption upon an attestation that the individual has been unable to enroll in such a plan through such exchange for a month in such year.