When a ball is hit foul is it still considered live?

A foul tip is a live ball if the catcher catches the ball. Otherwise, it is a dead ball.

According to the rules set by Major League Baseball:

A FOUL TIP is a batted ball that goes sharp and direct from the bat to the catcher's hands and is legally caught. It is not a foul tip unless caught and any foul tip that is caught is a strike, and the ball is in play. It is not a catch if it is a rebound, unless the ball has first touched the catcher's glove or hand.

6.05 A batter is out when-

(b) A third strike is legally caught by the catcher;

Rule 6.05(b) Comment: "Legally caught" means in the catcher's glove before the ball touches the ground. It is not legal if the ball lodges in his clothing or paraphernalia; or if it touches the umpire and is caught by the catcher on the rebound.

If a foul-tip first strikes the catcher's glove and then goes on through and is caught by both hands against his body or protector, before the ball touches the ground, it is a strike, and if third strike, batter is out. If smothered against his body or protector, it is a catch provided the ball struck the catcher's glove or hand first.

Rule 7.08(d) Comment: Runners need not "tag up" on a foul tip. They may steal on a foul tip. If a so-called tip is not caught, it becomes an ordinary foul. Runners then return to their bases.

5.09 The ball becomes dead and runners advance one base, or return to their bases, without liability to be put out, when-

(g) A pitched ball lodges in the umpire's or catcher's mask or paraphernalia, and remains out of play, runners advance one base;

Rule 5.09(g) Comment: If a foul tip hits the umpire and is caught by a fielder on the rebound, the ball is "dead" and the batsman cannot be called out. The same shall apply where such foul tip lodges in the umpire's mask or other paraphernalia.