This letter is concerned with the study of the $K^-_{stop}Arightarrow pi^pmSigma^mp A$ reaction in p-shell nuclei, i.e., $^{6,7}Li$, $^9Be$, $^{13}C$ and $^{16}O$. The $pi^pmSigma^mp / K^-_{stop}$ emission rates are reported as a function of $A$. These rates are discussed in comparison with previous findings. The ratio $pi^-Sigma^+/pi^+Sigma^-$ in p-shell nuclei is found to depart largely from that on hydrogen, which provides support for large in-medium effects possibly generated by the sub-threshold $Lambda(1405)$. The continuum momentum spectra of prompt pions and free sigmas are also discussed as well as the $pi^pmSigma^mp$ missing mass behavior and the link with the reaction mechanism. The apparatus used for the investigation is the FINUDA spectrometer operating at the DA$Phi$NE $phi$-factory (LNF-INFN, Italy).