Confining light into subwavelength volumes for long periods of time has been extensively pursued in the field photonics. In a recent work [Phys. Rev. A 89, 023813 (2014)], we demonstrated that the embedded eigenstates supported by open bi-layered plasmonic nanostructures may offer a unique opportunity to trap light with no radiation loss. In this paper, we investigate the impact of the spatial dispersion effects in the plasmonic shell in the emergence of the embedded eigenstates. Interestingly, it is found that the nonlocal effects offer new degrees of freedom for the material and geometrical parameters needed to have embedded eigenstates with infinite lifetimes. Particularly, thanks to the spatial dispersion effects, it is no longer necessary to have a shell with exactly zero-permittivity. Moreover, it is shown that a spatially dispersive core-shell nanoparticle may support multiple trapped states for the same geometry, rather than a single embedded eigenstate as in the local case.