Total absorption spectroscopy is used to investigate the beta-decay intensity to states above the neutron separation energy followed by gamma-ray emission in Br-87,Br-88 and Rb-94. Accurate results are obtained thanks to a careful control of systematic errors. An unexpectedly large. intensity is observed in all three cases extending well beyond the excitation energy region where neutron penetration is hindered by low neutron energy. The gamma branching as a function of excitation energy is compared to Hauser-Feshbach model calculations. For Br-87 and Br-88 the gamma branching reaches 57% and 20%, respectively, and could be explained as a nuclear structure effect. Some of the states populated in the daughter can only decay through the emission of a large orbital angular momentum neutron with a strongly reduced barrier penetrability. In the case of neutron-rich Rb-94 the observed 4.5% branching is much larger than the calculations performed with standard nuclear statistical model parameters, even after proper correction for fluctuation effects on individual transition widths. The difference can be reconciled by introducing an enhancement of 1 order of magnitude in the photon strength to neutron strength ratio. An increase in the photon strength function of such magnitude for very neutron-rich nuclei, if it proves to be correct, leads to a similar increase in the (n, gamma) cross section that would have an impact on r process abundance calculations