We study an inflationary supply shock in an economy with a high amount of private sector debt. In our framework, the central bank cannot control inflation by raising the interest rate sharply after the shock as doing so would trigger a debt crisis. It therefore follows a "backstop approach" of raising the interest rate sufficiently slowly so that the debt crisis is marginally avoided. We show that this backstop approach invites equilibrium multiplicity. Once agents expect the central bank to respond slowly to inflation, interest rate expectations fall, keeping private leverage high. As this constrains the central bank even more, inflation remains high for longer than fundamentals alone would imply. We derive these insights in a Keynesian growth model with financial frictions, calibrated to the recent Covid inflation crisis.