Taz, an adult pro parent, asks:
Is there ever a situation where a cautionable offense doesn’t require a stoppage of play, other than advantage?
Example: Player on Team A commits an unsporting behavior while their team has the ball, but they do not commit a foul. Is it required for the ref to stop play to issue the caution, or can the ref hold till the next stoppage of play?
Regarding your initial question, yes.
The 2019-2020 Laws of the Game, Law 12, provides that the usual procedure in a card situation is that the card is given at the very next stoppage – whether that is coincident with the commission of the misconduct or, if advantage is used, at the first stoppage following the misconduct either upon deciding that the advantage was not maintained for at least several seconds or, if play proceeds because the giving of advantage was successful, at the next stoppage whistled for any reason. The International Board long ago, though, advised referees that this should be a very rare occasion if the offense was a red car, the misconduct was violent, and there was little or no likelihood of an immediate goal being scored by the non-offending team.
There is a new “however” however – if (a) the non-offending team is ready, willing, and able to restart quickly; and (b) allowing the restart involves a clear goal-scoring opportunity; and (c) the referee has not taken any overt action (by word or deed) indicating that the restart may not be taken, the restart can be allowed to occur, the card remains as a punishment, but giving the card can be delayed until the next stoppage. (a) and (b) are entirely based on the judgment of the referee while (c) includes such things as the referee pulling out or otherwise displaying a card as concrete evidence that the card is about to be given or the referee saying anything in a sufficiently public way as to be heard by members of either or both teams in the immediate vicinity of the restart location.
Another way of explaining (c) is that, if the referee shows any public indication that a card will be given and this is understood to require that the restart will be delayed, thus inducing either one or both teams to back away from taking or defending against the restart, then the card must be given immediately even if the team in possession of the restart would objectively had wanted to restart quickly in order to take advantage of a goal-scoring opportunity. In short, the referee was not reading play correctly or had done something to lead players to believe that the referee was going to show the card and thus cause players to “back off.”
Now, your “example” actually raises two different questions. First, can a referee ignore an offense (foul or misconduct) and not give a card at all? Yes. It’s not generally advisable but is entirely within the referee’s scope of authority and may be entirely warranted (e.g., the offense was trifling or “iffy”). Second, can a referee decide that a card is to be given but waits quietly and without notice the next stoppage? Not in accordance with standard protocol unless advantage is being applied. Standard protocol calls for fouls and/or misconduct be called and punished accordingly upon their occurrence unless the referee invokes advantage. It is considered incorrect mechanics to “secretly” decide a misconduct has been committed and then do nothing about it until play stops, either by the referee’s whistle or by the ball leaving the field.