There is none. At least I cannot think of one.  Blue needs to stay out of the way.

(Maybe if Y recklessly changes course and does not give B time and space to keep clear.... just maybe)

EDIT: OMG I forgot about The Zone!   

According rule 18, Yellow boat must give mark-room to Blue.
By 18.1 rule 18 applies: Both are required to leave the mark on the same side, both are in the zone and no exceptions (a)-(d) applies.
By 18.2 (b) Y (outside boat) shall give B (inside boat) mark-room, because when Y reaches the zone, she was overlapped with B and was the outside boat.
Regards.

Y is the right of way (ROW) boat the entire time as Y is either leeward (RRS 11) or starboard (RRS10).  The boats are also overlapped the entire time (def overlap).  At position 2 when Y enters the zone RRS 18 turns on as none of the exceptions in RRS 18.1 is true.  Y, as an outside overlapped boat, is obligated to give B mark-room under RRS 18.2(b) even though Y is the ROW boat.  B is obligated to sail her proper course to the mark and not take any more room than necessary.  If Y has to gybe to give B the required mark room then that is what she must do to meet her obligation under RRS 18.2(b).

In this case Y would be penalized for breaking RRS 18.2 and RRS 14 and B would be exonerated for not keeping clear of Y (RRS 10) and the mark (RRS 31) under RRS 21.  It is also likely that B would not have broken RRS 14 as it would be unlikely that she could have avoided the contact.

Agree with Juan - Y is right-of-way boat (RRS 11, then 10), but owes mark-room to B per RRS 18.2(b). They are overlapped at the zone (see particularly the last sentence of the definition of Clear Astern and Clear Ahead; Overlap), and 18 applies between them.

Y could have gybed without her boom hitting B at the zone (pos. 2) when it became clear she would have to give room to B, and she failed to do so.

B is therefore exonerated for her breach of RRS 10 under RRS 21(a), and for her breach of RRS 31 under RRS 21(b). Y has failed to give B the mark-room to which she was entitled. Her having a crewman on the boom was likely unseamanlike (since it prevented her from giving room), and her concern about her boom hitting B if she gybed too late is immaterial, except it likely meant she waited to long to start giving B the mark-room B was owed (possibly because she had a crew member preventing it).

Penalize Y.

I agree with Christman and Mooney. Penalty Y.

I generally agree with the consensus so far.  

But to play devil's advocate: if B remained so close to Y at all points after entering the zone that Y could not jibe without causing contact, would the outcome differ?  What should Y do in those circumstances?

Being clear that B is the right-to-mark-room and Y the right-of-way boat, since rule 18 applies (when Y reaches the zone), B is entiltled to sail her proper course. 
According with the draw, this is the course B is sailing. Y must keep clear. Of course B is breaking rule 10 and 31 but she is exonerated by ry rule 21.

18 applies from @2
Y must give mark room to B
In order to be able to give mark room, Y, sailing by the lee, needs to sail even lower or gybe.
Has blue created a situation by being so close that if yellow gybed their boom and spinnaker would hit blue, such that blue has infringed? Could that ever be the case?

Sam, I don't think your scenario gets Y off the hook. We can be reasonably sure that B did not obtain her overlap by tacking to windward of Y, so let's assume (we don't know) that she gained it by overtaking Y from clear astern. In that case, for 18.2(f) to be of any help to Y, it would have to have been impossible for Y to give room from the time the overlap began, not from the time Y entered the zone. I'm not sure what circumstances would impose that limitation, but they don't apply here, IMHO.

These are 18' catboats in moderate to heavy breeze. Having a crewman sitting on the boom while finishing in close quarters with another boat was probably foolish, as it seems to have severely impeded Y's ability to gybe, but it would also probably have prevented or at least slowed the gybe if Y sailed by the lee for the time necessary to give B room. If Y can't give room because she can't maneuver normally, that's her problem, in my view; B has no obligation to expect that a boat that owes her room can't bear away or gybe normally when it becomes necessary to do so.

Thanks, John.  I overlooked 18.2(f).  I think that covers it.

The comments about jibing seem like a red herring. Since these are cat boats -- i.e., just a mainsail -- Y could have easily borne away without jibing in order to give room to B.

I say this because, in Lasers, we regularly sail by-the-lee angles of up to 70 degrees, i.e., with the wind flowing almost straight across your main from leech to luff. We know this because we sail with wind indicators on our mast so we know when we're so far by the lee that we need to jibe. And we do this in winds from 5 to 20+ knots, covering the range of this situation.

I generally agree, Al, but I have two caveats:
1  - I'm not sure what the OP means by a "balloon gybe", and I wonder if these boats might not have spinnakers, as well as mains (it's entirely possible it's a phrase I'm unfamiliar with having nothing to do with spinnakers, of course).
2 - Not all catboats have unstayed rigs like the Laser, and some can't go wildly by the lee like a Laser can.

That said, I still think it's Y's problem, not B's.

Y’s Lesson:  Had Y understood her obligation under 18 to provide B mark-room, Y could have started making room at 1 or 2 and avoided.  

B’s Lesson: Had B understood that she was entitled to room and exoneration, she would have known that she didn’t need to do 2 turns and finish a 2nd time. 

BIG Lesson to Y:  If Y was in the right, she could have gybed away, avoided contact and protested B. She would have lost the protest, but avoided risking damage and injury. 

I'd add one more lesson for Y. As long as she hadn't established her overlap from clear astern within two boatlengths of B (and RRS 17 didn't apply to her), Y could have luffed B (while giving her room to keep clear) before they reached the zone, such that after she stopped luffing and gybed to return to her course toward the finish, B would have been clear astern of her as they entered the zone, and not entitled to room at the finish mark.

That too would have involved getting the crew off the boom.

Thank you all for your comments!. I think we are now well versed on the 3 boat circle overlap and giving room. That being said, a couple responses to some of the speculations. Bcats are heavy and slow (mostly) with a single sail and no vang. A balloon gybe or accidental gybe is when the sail catches so much wind, the boom goes up almost parallel with the mast and comes down on the opposite tack. It's usually a violent action. Sometimes the sail can get wrapped around the mast or the gaff or tangled in rigging, etc. Crew sitting on the boom during a moderate wind downwind leg is standard practice for this class. (Both boats had crew on the boom) While it does not preclude a gybe (crew either circles the mast or hits the deck) it does add an additional safety element. Based on your comments, there seems to be consensus that Y boat should have gybed to give room. Y boat contends that would have required that B boat give room in order to avoid his boom. Given the circumstance, I'm not sure he would have done it differently, even if it was wrong. Again, thank you all. Hopefully this never happens again! ha. 

While at position 1, yellow is the ROW boat, she must forecast that from position 2 she owes B mark room. From the diagram, it seems that at pos. 2 Y is still able to separate from B and gibe if necessary. In not doing so, Y must be penalized.

In the case of Blue, when at pos 3 she realizes that Y is not going to comply her duty, she has to change  course to avoid contact (R. 14) and protest Y later.

Generally I agree but lets go to a new level.
Firstly the outside r.o.w boat does not have to give the mark room  until 18 applies and the other boat should keep clear.
If the boats are so close that the r.o.w has to alter course (before the zone) then they are not keeping clear and are to be penalised at that point. No later mark room can save them.

Michael, that’s the rub isn’t it?  The details matter significantly in this case. 

Interested, do you know of a Case/Appeal that interprets keep-clear’s ‘change course in either direction’ to include room to anticipate a “step function” change in separation-needed created by a Cat-boom’s huge overhang changing sides? (OP’s contention).

I seem to recall a Case/Appeal which discusses spinnakers collapsing and keep-clear. Maybe there is a tasty-nugget in that one to chew on to defend OP’s contention. 

PS:  I can’t seem to find the case/appeal I’m thinking of. Does this ring anyone’s bell?

Actually, here’s an interesting question.

By the OP description (not shown in the drawing), B hits the mark and Y, does turns and finishes after Y.  Thus, let’s assume that B crossed the finish line in the proper direction 2x AND that the RC did the correct thing and recorded 2 finish times for B. 

Though B did turns and crossed 2x, B validly protests Y. The PC finds there was no damage or injury and no Rule 2 violation.  PC exonerates B for 10, 14, 31 and DSQ’s Y for 14, 18. 

Q: Did B, by taking turns and crossing a 2nd time, continued to sail the course?  If so, and given the facts, is there a potentially successful avenue for B (Scoring inquiry, PC process, etc) to have B’s first crossing used?

I think there is an answer to this, you take a penalty when you may have broken a rule not when you have.
If you take a penalty therefore you always finish after the turns even if you are found later not to be at fault.
It is like insurance and limits any potential loss.
Yes she is continuing to sail the course to do he penalty, this removes the first finish and allows only the second. See definition of finish (c).

Thanks Mike, that’s what I thought.  Interesting game-play there for B.  In a large crowded OD fleet where 2 turns and re-cross the finish could cost you 1/4 of the fleet, that’s costly insurance.  On the other hand, in a smaller spread-out fleet, maybe it only costs 1-2 places.

Real good example of how confidence in ones knowledge of the rules can make a dramatic impact. 

And to put a fine point on it, the above facts are inconsequential.  If the PC did find one of those conditions existed, and used that as a justification to reinstate the first finish crossing, that in itself would be an improper action (as it’s hard to envision a scenario with the circumstances or facts that would necessitate or compel B to do turns and refinish). 

Kitchen table discussion finds that had Y gybed when B gybed, in order to give room for the mark, B would have potentially no longer had overlap with Y's stern. (Position 2)
We agree the minute details of the overlap/mark circle and at what point B accidentally gybed, all factor heavily and will certainly keep all of that in mind moving forward. 
Seems simple...hmm, maybe not so simple. 
PS I believe B lost three boats in that finish. Still won the regatta, with Y finishing 2nd overall. Thank you again for the discussion. We love the benefit of your expertise!