Why should the team whose player threw the ball away get any benefit at all?
They aren't getting a benefit. The ball is live and they have to hunt the ball down and make a play. Also, the penalty of throwing the ball away is that the batter who would've been out already got a base. Going from there is a risk to both teams. Proceed at your own discretion.
Would you also like the runners who take off on a steal to be able to stop if they don't get the right jump and go back to the base without risk of being thrown out?