Substitutes are extra players who may replace team-mates during a game. (see: Substitutions)
What happens if...
Any player arriving after kick-off may play, as long as their name was on the team list given to the referee before the game.
The game must be abandoned and a report to the appropriate authorities must be submitted after the game.
The referee must stop the game, reduce the team to the correct number and submit a report after the game to the appropriate authorities.
The extra player must be removed from the pitch and:
if the game has not restarted, the goal is disallowed, and play is restarted with a direct free kick to the other team from the position of the extra player
if the game has restarted, the goal is allowed, play continues, and the matter is reported to the appropriate authorities after the game
See also: ‘Substitutes or team officials on the pitch’
The extra player must be removed from the pitch and:
Play continues
Both players are shown a yellow card the next time the game stops