Dense suspensions often become more dilute as they move downstream through a constriction. We find that as a shear-thickening suspension is extruded through a narrow die and undergoes such liquid migration, the extrudate maintains a steady concentration ϕ_{out}^{LM}, independent of time or initial concentration. At low volumetric flow rate Q, ϕ_{out}^{LM} is a universal function of Q/r_{d}^{3}, a characteristic shear rate in the die of radius r_{d}, and coincides with the critical input concentration for the onset of LM, ϕ_{in}^{crit}. We predict this function by coupling the Wyart-Cates model for shear thickening and the "suspension balance model" for solvent permeation through particles.