Using a 2.5-dimensional, time-dependent ideal magnetohydrodynamic model in spherical coordinates, we present a numerical study of the property of magnetostatic equilibria associated with a coronal magnetic flux rope embedded in an axisymmetrical background magnetic field. The background field is potential (either closed or partly opened), a magnetic flux rope emerges out of the solar surface, and the resultant system is allowed to relax to equilibrium through numerical simulation. It is shown that the flux rope either sticks to the solar surface so that the whole magnetic configuration stays in equilibrium or escapes from the top of the computational domain, leading to the opening of the background field. Whether the rope remains attached to the solar surface or escapes to infinity depends on the magnetic energy of the system. The rope sticks to the solar surface when the magnetic energy of the system is less than a certain threshold, and it escapes otherwise. The threshold is slightly larger than the open limit, i.e., the magnetic energy of the corresponding fully opened field. The gravity, say, associated with the prominence mass, will raise the threshold by an amount that is approximately equal to the magnitude of the excess gravitational energy associated with the prominence. It implies that a catastrophe occurs when the magnetic energy of the system exceeds the threshold. The implication of such a catastrophe in coronal mass ejections is briefly discussed.