We present the study of five `dying nearby radio galaxies belonging to the WENSS minisurvey and to the B2 bright catalogs: WNB1734+6407, WNB1829+6911, WNB1851+5707, B2 0120+33, and B2 1610+29. These sources have been selected on the basis of their extremely steep broad-band radio spectra. The modeling of the integrated spectra and the deep spectral index images obtained with the VLA confirmed that in these sources the central engine has ceased to be active for a significant fraction of their lifetime although their extended lobes have not yet completely faded away. We found that WNB1851+5707 is in reality composed by two distinct dying galaxies, which appear blend together as a single source in the WENSS. In the cases of WNB1829+6911 and B2 0120+33, the fossil radio lobes are seen in conjunction with a currently active core. A very faint core is detected also in a MERLIN image of WNB1851+5707a, one of the two dying sources composing WNB1851+5707. We found that all sources of our sample are located (at least in projection) at the center of an X-ray emitting cluster. Our results suggest that the duration of the dying phase for a radio source in cluster can be significantly higher with respect to that of a radio galaxy in the field. The simplest interpretation is that the low-frequency emission from the fading radio lobes last longer if their expansion is somewhat reduced or even stopped. Another possibility is that the occurrence of dying sources is higher in galaxy clusters. Radio sources in dense environment, like e.g. the center of cooling core clusters, may have a peculiar accretion mode which results in a bursting duty cycle sequence of active and quiescent periods. This result could have important implications for theories of the life cycles of radio sources and AGN feedback in clusters of galaxies but awaits confirmation from future observations of larger samples of objects.