The first complete measurement of the β-decay strength distribution of _{17}^{45}Cl_{28} was performed at the Facility for Rare Isotope Beams (FRIB) with the FRIB Decay Station Initiator during the second FRIB experiment. The measurement involved the detection of neutrons and γ rays in two focal planes of the FRIB Decay Station Initiator in a single experiment for the first time. This enabled an analytical consistency in extracting the β-decay strength distribution over the large range of excitation energies, including neutron unbound states. We observe a rapid increase in the β-decay strength distribution above the neutron separation energy in _{18}^{45}Ar_{27}. This was interpreted to be caused by the transitioning of neutrons into protons excited across the Z=20 shell gap. The SDPF-MU interaction with reduced shell gap best reproduced the data. The measurement demonstrates a new approach that is sensitive to the proton shell gap in neutron rich nuclei according to SDPF-MU calculations.