I think there's a genuine ambiguity here. I looked at my 2012-2014 BCA league rules again (sorry, I'd copy-paste more of it but I can't find an online version right now), and it's clear from 1-43 and 1-44 that a) unscrewing is a concession and b) it not only is loss of game but also gets you a warning the first time you do it and loss of the game plus an additional penalty game if you do it again.
However, 1-41 covers coaching. The ambiguity comes from the fact that part 1. says there is no "assistance in planning or executing any shot," which is pretty narrow and doesn't seem to me to cover this situation, but the other parts refer simply to "assistance" which to me does cover someone saying "hey, your opponent just conceded." APA rules, which from my limited experience seem to allow more input from teammates and coaches, may be different.
In the end, I'd say it may be a coaching foul, but it's also loss of game, so the coaching foul would be moot.
edit: I found the relevant parts online:
1-41 Coaching
1. During your match, it is a foul if you ask for, or intentionally receive, assistance in planning or executing any shot.
2. It is a foul if you receive unsolicited assistance from a spectator associated with you (e.g., spouse/partner, relative, teammate). “Assistance” includes being alerted to an opponent’s foul.
3. If you are not aware of an opponent’s foul, and you are alerted to the foul by unsolicited information from a spectator not associated with you, the foul is not enforceable but you do not incur any additional penalty.
Exception: In scotch doubles or team play, a violation of Rule 1.8, No Practice Allowed During Match, may be called on any member of the opponent’s team by any member of the offended team, regardless of whether they or the offending player are at the table or involved in a game. Other modifications of this Rule 1-41 concerning team or doubles play may be made by the Administrative Authority.
4. Any spectator not associated with you who offers any significant assistance to you, whether verbal or non-verbal, will be
interruptions or removed from the area.
5. The Administrative Authority of the event may modify this rule for team or doubles play. (AR p. 92)
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1-43 Concession of Game
1. You must not concede any game at any time for any reason. “Concede” means that, as a result of any verbal or non-verbal action, you lead your opponent to believe that you are awarding them the game before its normal conclusion on the table. Before a game has ended, you must refrain from making any statements such as “good game”, etc., or any other verbal inference that the game is over or that your opponent is certain or likely to win. You must also refrain from any similar non-verbal action, such as putting away your cue or accessory items, beginning to mark a score sheet, changing clothes, retrieving or juggling coins or tokens, etc. Whether or not you have conceded a game is determined solely by the referee’s judgment.
2. If you concede a game, in addition to losing that game you will receive a mandatory warning against further concessions. A second violation results in the loss of the conceded game and an additional deduction of one game from your score (if you have zero games, your score would be "minus one game") and a final mandatory warning. A third violation results in loss of match. In team play, any member of the team may commit the second or third violations. (AR p. 92)
3. In the absence of any act by your opponent judged to be a concession under Rule 1-43- 1, you must not assume that your opponent has conceded the game. If you disturb the table in such a situation, then you are charged with a concession violation. (AR p. 92)
4. If you disturb the position of the table in an act that presumes the game is over before it is actually over, such as gathering balls together to rack the next game, you lose the game. (AR p. 92)
1-44 Concession of Match
When your opponent is on the hill, if you make a motion to unscrew your playing cue during your opponent's inning you lose the match. (AR p. 93)
However, 1-41 covers coaching. The ambiguity comes from the fact that part 1. says there is no "assistance in planning or executing any shot," which is pretty narrow and doesn't seem to me to cover this situation, but the other parts refer simply to "assistance" which to me does cover someone saying "hey, your opponent just conceded." APA rules, which from my limited experience seem to allow more input from teammates and coaches, may be different.
In the end, I'd say it may be a coaching foul, but it's also loss of game, so the coaching foul would be moot.
edit: I found the relevant parts online:
1-41 Coaching
1. During your match, it is a foul if you ask for, or intentionally receive, assistance in planning or executing any shot.
2. It is a foul if you receive unsolicited assistance from a spectator associated with you (e.g., spouse/partner, relative, teammate). “Assistance” includes being alerted to an opponent’s foul.
3. If you are not aware of an opponent’s foul, and you are alerted to the foul by unsolicited information from a spectator not associated with you, the foul is not enforceable but you do not incur any additional penalty.
Exception: In scotch doubles or team play, a violation of Rule 1.8, No Practice Allowed During Match, may be called on any member of the opponent’s team by any member of the offended team, regardless of whether they or the offending player are at the table or involved in a game. Other modifications of this Rule 1-41 concerning team or doubles play may be made by the Administrative Authority.
4. Any spectator not associated with you who offers any significant assistance to you, whether verbal or non-verbal, will be
interruptions or removed from the area.
5. The Administrative Authority of the event may modify this rule for team or doubles play. (AR p. 92)
--
1-43 Concession of Game
1. You must not concede any game at any time for any reason. “Concede” means that, as a result of any verbal or non-verbal action, you lead your opponent to believe that you are awarding them the game before its normal conclusion on the table. Before a game has ended, you must refrain from making any statements such as “good game”, etc., or any other verbal inference that the game is over or that your opponent is certain or likely to win. You must also refrain from any similar non-verbal action, such as putting away your cue or accessory items, beginning to mark a score sheet, changing clothes, retrieving or juggling coins or tokens, etc. Whether or not you have conceded a game is determined solely by the referee’s judgment.
2. If you concede a game, in addition to losing that game you will receive a mandatory warning against further concessions. A second violation results in the loss of the conceded game and an additional deduction of one game from your score (if you have zero games, your score would be "minus one game") and a final mandatory warning. A third violation results in loss of match. In team play, any member of the team may commit the second or third violations. (AR p. 92)
3. In the absence of any act by your opponent judged to be a concession under Rule 1-43- 1, you must not assume that your opponent has conceded the game. If you disturb the table in such a situation, then you are charged with a concession violation. (AR p. 92)
4. If you disturb the position of the table in an act that presumes the game is over before it is actually over, such as gathering balls together to rack the next game, you lose the game. (AR p. 92)
1-44 Concession of Match
When your opponent is on the hill, if you make a motion to unscrew your playing cue during your opponent's inning you lose the match. (AR p. 93)
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