Total absorption gamma-ray spectroscopy is used to measure accurately the intensity of γγ emission from neutron-unbound states populated in the ββ-decay of delayed-neutron emitters. From the comparison of this intensity with the intensity of neutron emission a constraint on the (n, γγ) cross section for highly unstable neutron-rich nuclei can be deduced. A surprisingly large γγ branching was observed for a number of isotopes which might indicate the need to increase by a large factor the Hauser-Feshbach (n, γγ) cross-section estimates that impact on r process abundance calculations.