Following the over fences class, the horses that pin will be called back for the jog in the order they are pinned. If the horses all jog sound, the placings stand. If a horse jogs lame, they will be spun and everyone behind them will move up in placings.
Also, if it's a class where conformation is judged, the final order for ribbons may be changed before the class is pinned. But the horses must demonstrate soundness in the jog before the conformation becomes a factor.