The distorted spin-dependent spectral function of a nucleon inside an A=3 nucleus is introduced as a novel tool for investigating the polarized electron scattering off polarized $^3$He in semi-inclusive DIS regime (SiDIS), going beyond the standard plane wave impulse approximation. This distribution function is applied to the study of the spectator SiDIS, $vec{^3{rm He}}(vec e, e ~{^2}{rm H})X$, in order to properly take into account the final state interaction between the hadronizing quark and the detected deuteron, with the final goal of a more reliable extraction of the polarized parton-distribution $g_1(x)$ inside a bound proton. Our analysis allows to single out two well-defined kinematical regions where the experimental asymmetries could yield very interesting information: the region where the final state effects can be minimized, and therefore the direct access to the parton distributions in the proton is feasible, and the one where the final state interaction dominates, and the spectator SiDIS reactions can elucidate the mechanism of the quark hadronization itself. The perspectives of extending our approach i) to the mirror nucleus, $^3$H, for achieving a less model-dependent flavor decomposition, and ii) to the asymmetries measured in the standard SiDIS reactions, $vec e + vec{^3 {rm He}} to e + h+X$ with $h$ a detected fast hadron, with the aim of extracting the neutron transversity, are discussed.
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