We study an optimal stopping problem (OSP) for Gauss–Markov processes conditioned to adopt a prescribed terminal distribution. By applying a time-space transformation, we stablish that this OSP is equivalent to that of a Brownian bridge with a random pinning point. These problems are scarcely addressed in the literature, not only due to the time-inhomogeneity of the underlying process and the non-Lipschitz, explosive behavior of its drift coefficient near the terminal time, but also because they deviate from the conventional monotonic optimal stopping boundary (OSB) framework. Furthermore, the OSB cannot even be regarded as the graph of a unique function in general, and its form depends on the process’s initial state at the time of conditioning. This is a joint work with B. D'Auria from the University of Padova.