The Crab and other pulsars suffer sudden and permanent increases in their spin-down rates in association with glitches, suggesting that the external torque on these objects grows in steps. Here, we describe how torque changes may arise from starquakes, occurring as the star spins down and its rigid crust becomes less oblate. We study the evolution of strain in the crust, the initiation of starquakes, the effects on the magnetic field geometry, and possible observable consequences for neutron star spin down. We find that the stellar crust begins breaking at the rotational equator, forming a fault inclined at an angle to the equator and directed toward the magnetic poles. The resulting asymmetric matter redistribution produces a misalignment of the angular momentum and spin axes. Subsequently, damped precession to a new rotational state increases the angle between rotation and magnetic axes. The change in this angle could increase the external torque, producing a permanent increase in the spin-down rate.