Using two-dimensional magnetohydrostatic equilibium theory, together with flux, entropy, and topology conservation, we demonstrate that a finite boundary deformation of magnetotail equilibria can lead to locally infinite current density enhancement, that is, the formation of a singular current sheet. Equilibrium configurations that satisfy the constraints cease to exist when the boundary deformation exceeds the critical value. This provides a strong argument for the onset of instability or the loss of equilibrium, regardless of the dissipation mechanism. The major feature causing the current density increase appears to be the localized increase of the boundary flaring angle, rather than the absolute magnitude of the boundary deformation. Such boundary perturbations might be caused by a solar wind pressure variation or suitable changes of the boundary electric field. Catastrophe points can be reached even for relatively small perturbations of the boundary. In those cases the excess energy associated with the thin current sheet is small. Nevertheless, a major disruption may be triggered when the underlying configuration becomes unstable upon the local breakdown of ideal MHD.