In football, the goalkeeper can cross the half-court line, but he can only move in his own half and midfield, and cannot enter the opponent's half. If a goalkeeper crosses the halfway line into the opposition half, he will be deemed offside. Unless the goalkeeper has a clear attacking mission, the goalkeeper usually does not cross the halfway line, as doing so would put the team at more risk in terms of offensive organization and defensive defense.
In practice, the rules allow goalkeepers to participate in the attack through the half, but this is very rare. According to the rules of football, the goalkeeper can participate in the attack like any other player, including crossing the halfway line and entering the opposing half. However, this usually only happens when the game is coming to an end and the result is critical, and they only cross the halfway line when the ball is passed to the goalkeeper in an emergency. And, in this case, the goalkeeper must also follow the rules of the offense, such as the offside rule.
In general, it is a rare and tactical decision for a goalkeeper to cross the half court and participate in the attack, as the goalkeeper's main task on the field is to protect the goal, not to attack.