While studying SM, I was taught that weak force bosons $V=\{W^\pm,Z^0\}$ do not interact with right/left-chiral fermions/antifermions. For this reason, we cannot observe right-handed neutrinos (if they do exist). However, we do observe right-chiral charged leptons as $e^-_R, \mu^-_R\dots$ through EM interactions (thanks to their charge).
But the decay of heavily charged leptons as $\mu$ and $\tau$ must involve weak force otherwise lepton family number would be violated,
\begin{equation}\label{eq1} \mu^-_L\rightarrow W^-+\nu_{\mu L} \rightarrow e^-_L+\bar{\nu}_{eR}+\nu_{\mu L} \quad \text{Involving weak bosons} \end{equation}
$$\mu\rightarrow e+\gamma \quad \text{Cannot happen since LFN is violated}$$
If right-chiral heavy fermions as $\mu_R^-$ and $\tau_R^-$ cannot decay through weak force? then how do they decay?