Large underground detectors, aimed at the search of rare processes, have the potential to contribute to the study of the next galactic supernova, by means of the study of neutrino-induced nuclear recoils. However, it is necessary to achieve continual sensitivity to the region of very low energies, above $\sim$ keV. An external trigger can be extremely valuable in this respect. The cases of off-line and on-line triggers are considered, making reference, respectively, to the existing SNEWS network and to a by-product of the operations of the LVD detector: the size of the memory buffer for temporary data storage, necessary in these two cases, is estimated.