Both ice hockey and football have penalty shots

now is the puck and the ball live after the shot is taken?
that is if the goalie does not control the ball or puck is the object considered live and anyone else can pounce on it to try and clear or score?

In hockey, you have to face-off after the shot.

Dead.

In Football( UK style - soccer to the US) the ball is live until it goes out of play
EG the penalty or free kick is taken - if it goes out of play it is dead and the game is restarted with the other team kicking/throwing back into play.

If the ball should stay in play (ie hit the post or a player and stay on the field of play) it is still "live" and can be played by any player of either team.

Basically - in soccer the ball is only out of play if it's "off the field" or the Referee has decided a team has infringed the rules.

Worth mentioning here the infamous Dutch penalty kick.

The only requirement of a football penalty is that the ball must travel forwards when kicked.

Cruyff (or Neeskens??) ran up to take the pen and just side footed a yard or so to his right (but slightly forwards) ... where another dutch player ran in and slotted it past a prostrate keeper.

This was replicated (at a slightly lower level) in a Bolton Pub Team Cup Semi (by a mate of mine). Basically the "kicker" ran over the ball using his studs to roll the ball slowly forwards. Another of his team was following up to put the ball home, again past a keeper flat on the floor. Score at the time was 3-3 and it transpired the pen won the match.

Quality.