What is the ruling on this?

In most cases, nothing.

The ball is still live and runners may advance at their own risk.

If for some reason the umpire feels that the runner intentionally interfered with the throw the runner will be called out for interference.

It's pretty hard to disguise a deliberate action on a ball in play as an "accident" as the runner would have to intercept the ball while it's in motion (the throw from home to second). Unless the timing was EXACT, the hesitation/change in speed/movement of the runner would be obvious and the runner will be called out on obstruction. Likewise if they moved a limb to steer it away from the fielder attempting to make a play on it.

If a thrown ball on any live play makes contact with a runner in the course of NORMAL play, it's not an out. INTENT DOES NOT MATTER for a call of Obstruction - if the ump feels for any reason the runner or batter-runner is obstructing the act of fielding, whether intentional or not, he's called out. This is why the call against the Red Sox in this year's World Series ending game 3 was correct. In your hypothetical situation, it is obstruction, by the book, even if it looks convincingly accidental.

My answer will be same as the others. And let me put this way. While (should be) running at his top speed to steal, if the stealing runner can deliberately get the ball away making it look accident, that's a great technique! This may sound dirty and I surely will not recommend/encourage young players to learn dirty tricks but play with fair sportsmanship. But that is clever play with great technique. It must be beyond obvious for a stealing runner to be called out for interference like as he got the 2nd base, the ball was right there and he flicks away and advances to 3rd base. Hey, how often do we see this? And how often do we see a batter pretending hit by pitch or get a runner out with fake tag?

If the ball goes beyond the reach of the shortstop or 2nd baseman, the runner will reach 2nd - perhaps even 3rd. If the runner intentionally allows the ball to hit him, the runner will be called out.

When a runner is touched by a thrown ball, ball is live, play on, unless the runner deliberately touches it.

Nothing. The baserunner is safe and wakes up the next day a little sore :)

SAFE!