Main panels: In-flux (black) and out-flux (orange) rates as a function of velocity contrast between the cloud and the interface (v_rel; left), cloud crushing time (t_cc; center left), vorticity in the interface (ω; center right), and the dot product between the magnetic tension vector and density gradient in the interface, i.e. the effective tension (f_T, eff = f_T ⋅ $\mathrm{\nabla }\widehat{\rho }$; right). The top panel shows the difference between the two, i.e. the net mass flow rate. While clouds with relatively low values of v_rel and ω experience a net in-flux of material, larger values of these properties trigger a net loss of cold gas from the cloud. The inverse trend holds for t_cc, as higher values correspond to larger shear times, thereby leading to a lower fraction of mass loss from the cloud. The strength and topology of magnetic fields may further be important, as a net magnetic tension force acting against the density gradient, i.e. away from the cloud and into the background, results in a net flux of mass into the cloud, likely by inhibiting the mixing of the background into the cloud.