On the field goal, the ball remains live until it is dead by rule. If the receiving team lets the ball die at the 10, it is the receivers ball at the 10.
But you wouldn't blow the whistle to kill the play if the ball lands at the 10 on a field goal. This is still a LIVE BALL.
If anyone is moving towards the ball or attempting to acquire the ball, just sit there and watch the ball and let the play complete. If the kicking team recovers, they have downed the ball, if the receiving team recovers, they can advance, fumble, whatever.
Only if nobody is going towards the ball, like everyone thinking the play is over, then kill the play, and give the ball to the receiving team where the ball is (the 10 yard line). In the NFHS, there is no such thing as moving the ball back to where it has been kicked like the NFL and NCAA.
If a field goal from the 40 yard line is missed wide-right through the back of the end zone, this is a TOUCHBACK. The ball is placed on the 20, not the 40.