Federal Unemployment Compensation Equality Act of 2019 This bill creates statutory authority for certain federal employees to be eligible for unemployment compensation during a lapse in appropriations. With respect to any lapse in appropriations beginning on or around December 22, 2018, a federal employee who is excepted from furlough (i.e., who continues to work during a lapse in appropriations) is deemed eligible for unemployment compensation benefits for the duration of the lapse in appropriations.