First, let me say that this is a purely hypothetical situation.
Let’s say a robot scales, but before the matches ends, a piece of their bumper completely falls off. The rest of their bumper is above the low goal, but the piece that fell off obviously is not. Per the rules, the robot is disabled, but they hold the elevated position. Is this a valid scale?
If a robot pushes its disabled alliance partner onto the batter, and then drives onto the batter at a different tower face, do both robots get credit for a challenge? Yes, they do. Or at least I have scored it that way, and seen it scored that way by other referees.
So a disabled robot can earn tower points. I think the situation you describe is similar.
 I think the piece that fell off is field debris, not part of the robot.[/edit]
I think that the question is more referring to the fact that since something fell off the robot, the part that fell off is below the top of the low goal, even though the rest of the robot is above it. Thus the part that fell off and is subsequently below the low goal would mean that not all of the robot is above the top of the low goal, and thus there would be no scale.
What the OP is asking is whether or not the piece that fell off counts as part of the robot. I don’t think that it would because once it fell off it would be considered field debrief and no longer part of the robot. Therefore the scale would count.
The problem is that this isn’t just some random piece of the robot - it’s a bumper. Does that make a difference? When a random chunk falls off the robot, it becomes a random chunk, while the robot continues on its way (containing everything it needs to be a ROBOT, per the definition). But does a BUMPER stop being a BUMPER if it falls off the robot? The definition FIRST provides does not require it to be attached to the robot to still be considered a bumper, merely designed to attach to the exterior of the robot. Even after falling off, it probably still meets that definition.
I would argue that even after falling off, a bumper is still a bumper. After all, if it falls off you can be disabled, while if your arm falls off you probably won’t be. So, per the scoring rules:
A ROBOT has SCALED the TOWER if, at the conclusion of the MATCH, the ROBOT:
A. is in contact with a unique RUNG, and
B. has all of its BUMPERS fully above the height of the low GOALS.
That bumper that fell off is not above the low goals, so I don’t think you should get the points.
If it were the bumper then I think that it probably wouldn’t count because the rules say all of the bumpers. So in that case I probably wouldn’t give the scale points but still give the challenge points.
When the bumper falls off, the fallen off part is no longer a bumper. The rule is that a robot will be disabled if it no longer meets the bumper rules. In theory, a robot could loose a non critical section of the bumper while still maintaining 8 inches on each corner, thus not be disabled.
In ruling whether it is a climb, I am not sure if you would look at just the remaining bumpers, or where the bumper would have been. I think the former.
Yes. If it is still attached, it still part of the bumper.
Not any different from the 15" rule. If it is attached, it counts. If it unitentionally detaches, it does not.
An interesting case is: Bumper partially detaches, drags for 1 second, and then full detaches. For 1 second, the robot is non-compliant with the Bumper Rules. However, by the time the Ref can disable the robot, it then becomes compliant.
For climbing rule purposes, there is the 5 second rule. So, if the bumper is still moving, the robot has not come to rest. If it detaches, then it is no longer a bumper part.
Given how most bumpers are constructed it’s not possible. However, it IS possible to construct bumpers for one side of the robot in three segments - 2 8" segments on the corner and a middle segment between them. That middle segment can fall off and your robot will still be compliant with the bumper rules.
One interpretation would be that a BUMPER (see Glossary) is “a protective assembly designed to attach to the exterior of the ROBOT and constructed as specified in Section 4 (4.7 BUMPER Rules).” A protective assembly that has become detached from the robot’s structure/frame no longer satisfies R26, and therefore no longer fits the definition of a BUMPER.
No rule *explicitly *addresses the case of a fallen-off bumper, and so a Q+A entry or blue-box addition would be required in order to enforce consistent management of a situation like this.
With that said, however, I believe that the game manual does provide a fairly solid foundation upon which said judgment can be founded:
Figure 4-3, “BUMPER corner examples” shows a section of bumper clearly labeled as being “NOT A BUMPER”. The sole reason given for this is that this section of bumper does not fulfill the requirements for placement with regard to the BUMPER PERIMETER, regardless of whether or not its construction otherwise meets all remaining requirements for a BUMPER.
I contend that the most reasonable interpretation will therefore be that any section of a ROBOT’S BUMPERS that ceases to fulfill the BUMPER rules during the course of a match is no longer considered a BUMPER, and should therefore be treated as either part of the robot or field debris (depending on whether or not it actually falls off), same as any other broken ROBOT component.