Abstract How pre‐existing solar wind turbulence, and coherent structures such as magnetic flux ropes within it, influence the transition of plasma across a shock is still poorly understood. Recently, in situ observations from the Earth’s magnetosheath have been used to study plasma stability against ion kinetic instabilities. In the turbulent flow, the state of the plasma varies but its distribution in a β‖ ${beta }{Vert }$–T⊥/T‖ ${T}{perp }/{T}{Vert }$ parameter space is generally bounded by contours of marginal stability from linear theory. Observations often report a sharp low‐β‖ ${beta }{Vert }$ boundary in such distributions, however no known instability is understood to limit the plasma in that regime. We use a hybrid simulation of a collisionless shock interacting with a turbulent flow and show that magnetic flux ropes populate the low‐β‖ ${beta }{Vert }$ limit of the distribution both in the upstream and downstream regions. The flux ropes are associated with distinct tracks in the β‖ ${beta }{Vert }$–T⊥/T‖ ${T}{perp }/{T}{Vert }$ distribution, following the double‐adiabatic prediction Tp⊥/Tp‖∝βp‖−3/4 ${T}{mathrm{p}perp }/{T}{mathrm{p}Vert },propto ,{beta }_{mathrm{p}Vert }^{-3/4}$.