Official BCAPL response
The ruling in BCAPL play (unfortunately for the shooter) is: bad luck. Play on. I believe that the ruling in WPA is the same, but will defer to them for a positive statement.
The current citation in BCAPL is Rule 1.49.1, Balls Settling or Moving: "If a ball settles or move by itself, it will be left in the position it assumed and play continues."
The current citation in WPA (as noted by Cuebacca) is Rule 1.7, Balls Settling: "A ball may settle slightly after it appears to have stopped, possibly due to slight imperfections in the ball or the table. Unless this causes a ball to fall into a pocket, it is considered a normal hazard of play, and the ball will not be moved back."
Although neither rules set currently explicitly addresses the situation at hand (ball settling
but not falling into a pocket while you are shooting at it) the historical interpretation has been: bad luck, play on.
The issue has been presented to the BCAPL National Office, and they are, after initial discussion, in agreement. It will be considered again during the final review of the 2009-2010 edition of the BCAPL Rules, but I do not anticipate a change. Whichever way they land, the exact situation will be specifically addressed and a positive ruling will be in place, either as an Applied Ruling or as a new portion of Rule 1.49.1.
It might also be noted (again, as Cuebacca did) that there could be a perceived discrepancy between that ruling and the ruling when a settling ball falls into a pocket as you are shooting at it. In that case, under BCAPL and WPA rules, the ball is usually replaced or there is another remedy available. However, there is a reasonable rationale for a different ruling when the event takes place without the ball falling.
First and foremost, a ball falling into a pocket is an undoubtedly quantifiable event. A ball settling slightly (or even a little more than slightly) is not. Not to impugn anyone's observation skills in any way, but if there were a dispute after the fact and another player said "no, I did not see it settle", the simple fact of the matter is that there is no way the movement can be verified. If it cannot be positively determined, it cannot be enforced.
Secondly, the event cannot be truly enforced equally across the board in all circumstances. Consider: you are playing 9-Ball. early in the game, the 2-ball is close to a pocket. After missing the 1-ball on a hard shot, another ball is tracking towards the 2-ball and preparing to strike it , but not at an angle that would pocket it. All of a sudden, the 2-ball settles and shifts to a position that causes it to be pocketed. Are you going to turn down the shot and replay the game? Not likely. The initial reaction of most people is going to be "wow - that was lucky".
Although it is the same principle in that example as in the OP's 8-ball shot, it is not uncommon for players to want to attach a different principle to a late-game or game-winning ball shot. It is natural, since the injustice is perceived to be greater. However, in this case you would be hard pressed to rationalize treating the two shots differently.
Finally, as Woody observes, there is no guarantee that the shot would have been made had the settling not occurred. (By the way Woody, it's time for a new book!

). Cuebacca observes that it might not be important, but then again it might be. Cuebacca's example, however departs into the world of interference, as do many other observations in the thread. Interference is an entirely different matter. The interference rules are written to account for non-player human interruptions or severe outside equipment contingencies (lights falling, etc.). The simple fact that there is a rule addressing balls settling indicates that interference is not applicable.
On a side note, despite the fact that OP states that the movement was caused by a fault in the table, under BCAPL and most other sets of rules, the equipment's condition was accepted once the game began and cannot be used as a reason to replay the specific shot.
Buddy Eick
BCAPL National Head Referee (WOW!! very humbled to be promoted :grin: )
BCAPL Director of Referee Training
Technical Editor, BCAPL Rule Book
bcapl_referee@cox.net
Find the Official Rules of the BCA Pool League here:
http://www.playbca.com/Downloads/Rul...2/Default.aspx
* The contents of this post refer to BCA Pool League (BCAPL) Rules only. The BCAPL National Office has authorized me to act in an official capacity regarding questions about BCAPL Rules matters in public forums.
* Neither I nor any BCAPL referee make any policy decisions regarding BCAPL Rules. Any and all decisions, interpretations, or Applied Rulings are made by the BCAPL National Office and are solely their responsibility. BCAPL referees are enforcers of rules, not legislators. BCAPL Rules 9.4.3 and 9.4.4 apply.
* No reference to, inference concerning, or comment on any other set of rules (WPA, APA, VNEA, TAP, or any other set of rules, public or private) is intended or should be derived from this post unless specifically stated.
* There is no such thing as "BCA Rules" other than in the sense that the Billiard Congress of America (BCA) publishes various rules, including the World Pool-Billiard Association's "World Standardized Rules". The BCA does not edit nor is responsible for the content of the World Standardized Rules. The Official Rules of the BCAPL is a separate and independent set of rules and, to avoid confusion, should not be referred to as "BCA Rules".
* Since 2004, there is no such thing as a "BCA Referee". The BCA no longer has any program to train, certify or sanction billiards referees or officials.
* The BCAPL has no association with the Billiard Congress of America other than in their capacity as a member of the BCA.
* The BCAPL has not addressed every imaginable rules issue, nor will it ever likely be able to, as evidenced by the seemingly endless situations that people dream up or that (more frequently) actually happen. If I do not have the answer to a question I will tell you so, then I will get a ruling from the BCAPL National Office and get back to you as soon as I can. If deemed necessary, the BCAPL will then add the ruling to the "Applied Rulings" section of The Official Rules of the BCA Pool League.