  We propose a novel probe of weakly interacting massive particle (WIMP) dark
matter (DM) candidates of a wide mass range which fall short of the required
annihilation rates to satisfy correct thermal relic abundance, dubbed as
\textit{Miracle-less WIMP}. If the DM interactions are mediated by an Abelian
gauge boson like B-L, its annihilation rates typically remain smaller than the
WIMP ballpark for very high scale B-L symmetry breaking, leading to
overproduction. The thermally overproduced relic is brought within observed
limits via late entropy dilution from one of the three right handed neutrinos
(RHN) present for keeping the model anomaly free and generating light neutrino
masses. Such late entropy injection leads to peculiar spectral shapes of
gravitational waves (GW) generated by cosmic strings, formed as a result of B-L
symmetry breaking. We find interesting correlation between DM mass and turning
frequency of the GW spectrum with the latter being within reach of future
experiments. The two other RHNs play major role in generating light neutrino
masses and baryon asymmetry of the universe via leptogenesis. Successful
leptogenesis with Miracle-less WIMP together restrict the turning frequencies
to lie within the sensitivity limits of near future GW experiments.
