In this contribution we summarize the recent study of the β decay of neutron-rich nuclei with isomeric states close in energy to the ground states. The disentanglement of each pair of β-decaying states was achieved by applying different strategies and using the purification capabilities of the JYFLTRAP double Penning trap system at the Ion Guide Isotope Separator On-Line facility in Jyvaskyla. The Total Absorption γ-ray Spectroscopy technique was employed to determine the β intensity probabilities populating the excited states in the daughter nuclei. Previously undetected β intensity was found and we have already evaluated the impact of part of these results on reactor summation calculations. The possibility to populate states associated with the Pygmy Dipole Resonance in the β decay of 96gsY has also been investigated thanks to the sensitivity of our technique to high-lying strength in the daughter nuclei.