Observations show that magnetic fields in the interstellar medium (ISM) often do not respond to increases in gas density as would be naively expected for a frozen-in field. This may suggest that the magnetic field in the diffuse gas becomes detached from dense clouds as they form. We have investigated this possibility using theoretical estimates, a simple magneto-hydrodynamic model of a flow without mass conservation and numerical simulations of a thermally unstable flow. Our results show that significant magnetic flux can be shed from dense clouds as they form in the diffuse ISM, leaving behind a magnetically dominated diffuse gas.