Its not only possible, but incumbent to do so! Economic and political instability usually implies a power vacuum which will be filled by demagogues across the political spectrum.

The hyperinflation and political humiliation suffered by the Weimar republic led to it being assailed by both the extreme left and the extreme right, until you know who, in the febrile political climate, grabbed the reigns of power.

Human nature craves security and will turn desperately to anyone who looks like they can deliver it. Better the devil you know (a democratic functioning state), then a despotic one.