Teams receive full fantasy credit for all stats accumulated at a position on the day the games played maximum is reached at a position.
So, if your league features three center positions and a games-played limit of 246 center (82 per center) games, a team could exceed that number if they started a day with 245 games used and played three centers the day the limit was reached.
Beginning the following day, no additional fantasy stats would be earned at those positions.