  KS-contextuality is a crucial feature of quantum theory. Previous research
demonstrated the vanishing of $N$-cycle KS-contextuality in setups where
multiple independent observers measure sequentially on the same system, which
we call Public Systems. This phenomenon can be explained as the additional
observers' measurements degrading the state and depleting the quantum resource.
This explanation would imply that state-independent contextuality should
survive in such a system. In this paper, we show that this is not the case. We
achieved this result by simulating an observer trying to violate the
Peres-Mermin noncontextuality inequality in a Public System. Additionally, we
provide an analytical description of our setup, explaining the loss of
contextuality even in the state-independent case. Ultimately, these results
show that state-independent contextuality is not independent of what happens to
the system in-between the measurements of a context.
