An adult/pro level referee asks:
A goal is scored in the 50th minute and, during the stoppage that results, the referee notices that the scorer had not been a player when the first half ended. Apparently, the scorer had swapped places with a teammate who had been a player at the end of the first half and then, as players were returning to the field for the start of the second half, entered the field in effect as a substitution that had not been brought to the referee’s attention. What should the referee decide?
First, this sort of thing should not happen, either as a result of referee inattention or as a breakdown in communications within the officiating team, all of whom have a collective and individual responsibility for ensuring that the Law’s requirements are met (see Law 3, section 3: “If a substitution is made during the half-time interval or before extra time, the procedure must be completed before the match restarts”).
Second, although this situation could theoretically occur in any match, it is much more likely to happen in a match which is not being governed by the strict substitution requirements of Law 3 … in other words, in a youth game where substitutions are usually unlimited and with a “right to return” (see, again, Law 3, section 2). Detailed recordkeeping of who enters and leaves under these common circumstances is often nonexistent because it is so cumbersome.
Third, following from the first two comments, it is highly likely that the “substitution” was not the result of a willful, intentional desire to circumvent the Law to gain an advantage or to show a lack of respect for the game.
Frankly, this situation is not directly or clearly covered by the Laws of the Game. You might think it is but it really isn’t. A student of the Law would likely point to Law 3, Section 5, which suggests that the scorer, having entered the field illegally (i.e., without the referee’s permission using standard substitution mechanics), should be cautioned and play restarted with an IFK where the ball was when play was stopped. This is fine if the entry had been during play, was seen, and play stopped for this infraction. Others might suggest that the situation is governed by Law 3, Section 7, which provides for sanctions in the case of an “extra person” who enters the field and interferes with play. But the scorer is not an “extra person” as that term is generally used. Here, the stoppage occurred solely because the ball left the field (into the goal — but it could just as easily been across the touchline for a throw-in restart.
“By the book,” there isn’t a clear answer. Is there something close? Consider the following: caution the scorer for entering the field without the referee’s permission, cancel the goal, require the scorer to leave the field and be replaced with the original player, and restart with a goal kick. This stitched-together set of referee actions is supportable by various sections of the Law and by the underlying intent of the Law.
For a match below the highest competitive levels (where, as suggested, this sort of thing is more likely to have occurred), there is, however, a fairly simple alternative. It is commonly understood that, when the referee signals for the start of the second half (as with the first half and all subsequent periods of play), this is an implicit confirmation that the referee (assisted by both ARs) accepts that all players are correctly on the field under Law 3, their uniforms and equipment meet the requirements of Law 4, and the field itself is acceptable under Law 1. The signal to start the period of play could thus be reasonably taken as an implicit acceptance of the player “substitution.” If this line of argument is persuasive, then the substitution has been tacitly accepted, the score stands and no caution for illegal entry is needed. Absent a belief by the referee that the “substitution” was undertaken for nefarious and unsporting purposes, why make things more difficult for everyone and for no particularly compelling reason? The player (and the player’s coach) could be reminded of their obligation to make sure in the future that the referee is more properly advised about any otherwise well-meaning substitution that had been made during a between periods break.
We hasten to add that the immediately preceding suggestion is not officially recognized and you are welcome to act according to your own conscience. However, we believe that the way Law 3, section 5 (“a named substitute starts a match instead of a named player and the referee is not informed of this change”) resolves this situation is in the same spirit in which our “simple solution” is offered.
Update: As of the 2017/2018 revisions to the Laws of the Game, the “common sense” answer suggested above has been approved by the International Board. The new version of the Laws of the Game provides that a substitution made during any break between periods of play (e.g., half-time) without the prior knowledge or approval of the Referee is to be accepted as valid and is not subject to a caution for misconduct.