The indeterminacy region amounts to implicit prior truncation. It is usually not an issue for the posterior. Exemptions are cases where this region creates a valley that the MCMC is not able to pass through to get to the other side. But usually that region extends to infinity, so that is usually not an issue.
Where prior truncation will create problems is for the model comparison via marginal data densities. Here you need to correct for prior not integrating to 1.