Momenta spectra of protons emitted following the capture of $K^-$ in $^6$Li and $^{12}$C have been measured with 1% resolution. The $^{12}$C spectrum is smooth whereas for $^6$Li a well defined peak appears at about 500 MeV/$c$. The first observation of a structure in this region was identified as a strange tribaryon or, possibly, a $bar K$-nuclear state. The peak is correlated with a $pi^-$ coming from $Sigma^-$ decay in flight, selected by setting momenta larger than 275 MeV/$c$. The $Sigma^-$ could be produced, together with a 500 MeV/$c$ proton, by the capture of a $K^-$ in a deuteron-cluster substructure of the $^6$Li nucleus. The capture rate for such a reaction is $(1.62pm 0.23_{stat} ^{+0.71}_{-0.44}(sys))%/K^-_{stop}$, in agreement with the existing observations on $^4$He targets and with the hypothesis that the $^6$Li nucleus can be interpreted as a $(d+alpha)$ cluster.
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