  Two of the most influential exact results in classical one-dimensional
diffusive transport are about current statistics for the symmetric simple
exclusion process in the stationary state on a finite line coupled with two
unequal reservoirs at the boundary, and in the non-stationary state on an
infinite line. We present the corresponding result for the intermediate
geometry of a semi-infinite line coupled with a single reservoir. This result
is obtained using the fluctuating hydrodynamics approach of macroscopic
fluctuation theory and confirmed by rare event simulations using a cloning
algorithm. Our exact result enables us to address the corresponding problem on
an infinite line in the presence of a slow bond and several related problems.
