Sorry, this is all I remember. A story where the end was a hail of micrometeorites all falling to Earth at once which incinerated the atmosphere from the collective heat from their re-entry. I think it was caused by either the moon being blown up or by a comet being destroyed by missiles.
I also think that it was called a "Soft Rain", but searching for a soft rain just gets me a different story about an automated house.
Any help on finding this story would be very much appreciated, this is one that's been on my mind for ages.