When Solar system passes through moderately dense interstellar clouds, Earth experiences a dramatic increase in the flux of the anomalous component of cosmic rays (ACRs) along with an increased flux of galactic cosmic rays. ACR flux across the Earth's orbit lasts as long as it takes to cross a moderately dense interstellar cloud, about 1 Myr years. A period of ~1 Myr is long enough for Earth to experience at least one magnetic reversal allowing penetration of the cosmic rays deep into the atmosphere even at low latitudes. Such increased cosmic ray fluxes would enhance the abundance of stratospheric NOx ~100 times between 20--40 km, which in turn would decrease the ozone column globally by at least 40% and in the polar regions up to 80%. Such ozone loss would last for the duration of the magnetic reversal and could trigger global extinctions.