Whenever a member of the kicking team touches a punt or place kick beyond the line of scrimmage before a member of a receiving team touches the ball, a bean bag is thrown by the covering official, indicating a spot of illegal touching. This spot is an insurance policy for the receivers and unless they foul and the penalty is accepted, they may take the ball at the spot of illegal touching or at the spot where the play ends, whichever is most advantageous for the receiving team. So, finally, in answer to your question, the receiving team can pick up and advance the ball after it has been illegally touched, and even if they fumble and the kickers recover, the receivers get the ball at the bean bag spot.