With the possibility of testing massive gravity in the context of black hole physics in mind, we consider the radiation produced by a particle plunging from slightly below the innermost stable circular orbit into a Schwarzschild black hole. In order to circumvent the difficulties associated with black hole perturbation theory in massive gravity, we use a toy model in which we replace the graviton field with a massive scalar field and consider a linear coupling between the particle and this field. We compute the waveform generated by the plunging particle and study its spectral content. This permits us to highlight and interpret some important effects occurring in the plunge regime which are not present for massless fields such as (i) the decreasing and vanishing, as the mass parameter increases, of the signal amplitude generated when the particle moves on quasicircular orbits near the innermost stable circular orbit and (ii) in addition to the excitation of the quasinormal modes, the excitation of the quasibound states of the black hole.

v2 : Minor changes to match the published version