Neal Stephenson wrote a book about that..

https://www.amazon.com/Seveneves-Novel-Neal-Stephenson/dp/00...

It will turn into a cloud of asteroids surrounding the earth intended to prevent the human race from unleashing whatever hell we create with those autonomous mining robots on the ISS (would be my guess, at least). Feel like the agent/patient distinction is pretty blunt foreshadowing against it being a survival/resilience story against and abstract antagonist like a random natural disaster.

edit: http://www.amazon.com/Seveneves-A-Novel-Neal-Stephenson/dp/0... gives a bit more detail and it is likely it will not become a ring. Probably a lot of highly energetic reentrant debris capable of generating a lot of atmospheric heat.

edit: @jaquesm - i'm allowing for creative license, and was making guess explaining what would happened based on my gut feel for the plot direction. you're probably correct on the physics.