Outlined is the discovery of a very faint, diffuse, low surface-brightness (0.5 mJy beam −1 , 1.4 mJy arcmin −2 on average) structure around the radio source B2 0258+35 hosted by an HI-rich early-type galaxy (NGC 1167). Because B2 0258+35 is a young compact steep spectrum (CSS) source, the newly discovered structure could represent a remnant from an earlier stage of activity of an active galactic nucleus (AGN). We explain in detail all possibilities for triggering the radio activity in B2 0258+35 regarding gas accretion in a recurrent AGN activity framework. NGC 1167 hosts a very regular, extended and massive H I disk that has been studied in great detail. It has regular kinematics on large scales, which, together with stellar population studies of NGC 1167, exclude the possibility of a recent merger as the trigger for the current AGN activity that is responsible for the CSS source. Previous studies of the H I closer to the core seem to preclude the assumption of a circum-nuclear disk of H I as the source of the accreting gas. We consider the cooling of gas from the hot X-ray halo as a possible alternative option for the fueling of the AGN, as suggested for other sources of similar radio power as B2 0258+35. This would provide a more likely explanation for the recurrent activity. Furthermore, if the previously made suggestion in the literature that the inner CSS may not be able to grow to large scales is correct, this implies that different cycles of activity may have different characteristics (e.g. radio power of the emission). Estimates are given for the age of the faint diffuse emission as well as for the current accretion rate, which agree well with literature values. If our assumptions about the accretion mechanism are correct, similar large-scale, relic-like structures should be more commonly found around early-type galaxies, which will hopefully be confirmed by the next generation of sensitive, low-frequency radio surveys.