Foreclosure Relief and Extension for Servicemembers Act of 2014 - Amends the Honoring America's Veterans and Caring for Camp Lejeune Families Act of 2012 to make permanent the extended one-year period after a servicemember's military service during which: (1) a court may stay proceedings to enforce an obligation on real or personal property owned by the servicemember prior to such military service; and (2) the sale, foreclosure, or seizure of such property is invalid without a court order or agreement. (Currently, the extended one-year period is scheduled to expire on December 31, 2014, and return to a nine-month period under the Servicemembers Civil Relief Act.)