The player at the line takes their second shot and as the ball hits the rim it bounces and gradually slows down and stops on the back square of the rim. Does the shooter get another shot or is the ball turned over, or does the posession arrow need to be used?

Go to the arrow, assuming it's the 2nd of two shots, and not the 2nd of three shots.

But take a picture first - I have never seen this and I would like to.

I must be an oddball
 

I have had the ball come to rest on the flange twice this year and usually see it at least two times a year.

I've had it happen. It's called a "false-wedgie".

I've even had a real wedgee on a free throw!

Hey thanks for the replys, but lets just say that this happened on the first free throw. Do you give them another shot at the first one or does it count as a missed basket.

First of two, just another miss.

A free-throw ends when it becomes obvious that it will not be successful. So, first free-throw ends unsuccessfully (with a false wedgie), move on to the second throw.