  The behaviour of boundary conditions under relevant bulk perturbations is
studied for the Virasoro minimal models. In particular, we consider the bulk
deformation by the least relevant bulk field which interpolates between the mth
and (m-1)st unitary minimal model. In the presence of a boundary this bulk flow
induces an RG flow on the boundary, which ensures that the resulting boundary
condition is conformal in the (m-1)st model. By combining perturbative RG
techniques with insights from defects and results about non-perturbative
boundary flows, we determine the endpoint of the flow, i.e. the boundary
condition to which an arbitrary boundary condition of the mth theory flows to.
