When the batter hits the ball into foul territory, and an opposing player catches it in foul territory on the fly.
There are lines placed to divide the foul territory and the fair territory. Any ball that lands on the foul territory will be called foul. When the ball enters the fair territory, ball is at play.
If the ball is in foul territory and hits a base runner in foul territory then it is a foul ball, so no he would not be out
There are basically three areas to consider here: fair territory, foul territory, and out-of-play territory. A ground foul ball is not playable. A fly foul ball is playable if it is not in out-of-play territory. A fly foul ball is not playable if it is in out-of-play territory. An example of out-of-play territory might be a dugout. Out-of-play territory should be defined by the rule book, the ground rules, or by the umpires prior to game time.
Foul territory is that part of the playing field outside the first and third base lines extended to the fence and perpendicularly upwards. A foul ball is a batted ball that settles on foul territory between home and first base, or between home and third base, or that bounds past first or third base on or over foul territory, or that first falls on foul territory beyond first or third base, or that, while on or over foul territory, touches the person of an umpire or player, or any object foreign to the natural ground.
Most of the batter's box is in foul territory, but some of it is in fair territory, so it depends where the batted ball comes to rest.
If the ball is in fair territory, the fact that the fielder is standing in foul territory does NOT make the ball foul. the same as if a ball is foul, the fielder standing in fair territory doesn't make the ball fair.
Foul ball
If the ball first lands in foul territory, then it is a foul ball. If the ball lands in fiar territory and rolls into the foul territory after first base, it's a fair ball. - So, if the ball is in the air in fair territory and drifts to foul after first base still in the air, makes first contact with the ground in foul territory, it's a foul ball.
as high as you can hit it in foul territory
If a batted ball lands in fair territory but then crosses the foul line BEFORE passing or touching first or third base, then it is a FOUL ball. If a batted ball lands in fair territory between first and third base, bounces in the air, and crosses into foul territory before passing first or third base, it is a foul ball, even if caught on the bounce in foul territory by the first or third baseman.
It's still foul cause the ball was hit in foul territory. Whether a ball is fair or foul is based on the position of the ball when it is touched. Since the ball was touched when the ball was in foul territory, it would be a foul ball.