Observations show that the magnetic field in the interstellar medium (ISM) of the Milky Way and other spiral galaxies does not respond to increases in gas density as would be naively expected for a frozen-in field. This has led to the suggestion that the magnetic field in the diffuse gas becomes detached from dense clouds as they form (Beck et al. 2005). We investigate this possibility using theoretical estimates, a simple magneto-hydrodynamic model of a flow without mass conservation and numerical MHD simulations of a thermally unstable flow in two and three dimensions. 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 phase. We also offer an explanation for the puzzling observations that measure the same magnetic field strength in interstellar gas spanning 4 orders of magnitude in density (Troland \& Heiles 1986).