The MHD instability of a current sheet created by the focusing of disturbances in the vicinity of a singular line is studied. The analysis allowed the total plasma mass in the sheet to vary with time. Its decrease leads to a redistribution of plasma density across the sheet thickness in such a way that the plasma density near the sheet boundary decreases. It is shown that the sheet becomes unstable if the plasma density near the sheet becomes sufficiently small. Possibilities of an intensification of the instability during the nonlinear phase are considered.