  This paper provides an exact simulation algorithm for the sampling from the
joint law of the first-passage time, the undershoot and the overshoot of a
subordinator crossing a non-increasing boundary. We prove that the running time
of this algorithm has finite moments of all positive orders and give an
explicit bound on the expected running time in terms of the L\'evy measure of
the subordinator. This bound provides performance guarantees that make our
algorithm suitable for Monte Carlo estimation. We provide a GitHub repository
with an implementation of the algorithm in Python and Julia.
