As estimation result of an AR coefficient, I get a posterior with mean 1 and zero confidence interval. This implies that also the mode must have been 1. But then, how di Dynare solve the model?
First of all, there must be something wrong here with your model.
Second, the Blanchard-Kahn conditions allow for unit roots as does the Kalman filter. The conditional variance still exists. So, there is no particular problem.