  In this article we investigate the fibers of relative $D$-modules. In general
we prove that there exists an open, Zariski dense subset of the vanishing set
of the annihilator over which the fibers of a cyclic relative $D$-module are
non-zero. Next we restrict our attention to relatively holonomic $D$-modules.
For this class we prove that the fiber over every point in the vanishing set of
the annihilator is non-zero. As a consequence we obtain new proofs of a
conjecture of Budur which was recently proven by Budur, van der Veer, Wu and
Zhou, as well as a new proof of a theorem of Maisonobe. Moreover, we also
obtain a diagonal specialization result for Bernstein-Sato ideals.
