People did a really great job with their responses and comments and most were close to the mark. It was an impressive effort and I would like to say thanks to those that took a guess and hope you can share more thoughts as more cases are presented.
As is always the case we need to be careful to not over generalize. That said, there is a certain consistency I have found both with my clients and in my own life in regards to this seemingly odd behavior.
The reason that the people become so distraught is they are still in love with the other person, but in their minds the relationship has come to the point where it must be left entirely. It is a way of wishing to say goodbye for good, but needing to be supported while they do it. Their former partners, who tend to have been supportive in the relationship, provide the ideal supportive function. It is an ideal shoulder to cry on, but they can never tell the other person that they are crying because they are about to vanish from the relationship completely.
There is a fair element of control involved in this dynamic. The person who broke off it initially maintains their illusion of control by withholding the reason why they are crying from the other person. Even though they appear distraught and out of control outwardly, the withholding mechanism provides a way in which they can manipulate the distance in the relationship. For example, if someone is crying but not stating the reason for their crying, it makes the other person involved wonder about what is going on. In turn, it makes that person want to try and fathom why the person is crying. Questions tend to follow, unconsciously the person begins to chase the other for the answers.
Why the dual breakups? The first break off is a break off, but both people still have a desperate need for intimacy. The first break off is a kind of a releasing the pressure cooker of the relationship. That is one function of it. The other function is that it provides a safer way for the people to take steps towards being apart. It is not a clean break, rather it is a type of gradual walking away, where some sex and intimacy remains but without the commitment.
The second break off occurs because the person realizes that there actually has to be a “clean break off”. This second break off may not occur for some time after the crying. The crying is more the recognition point of “I need to be completely apart from this relationship”.
Why not cry and grieve with their family and friends instead? That will usually occur anyway. It’s just that in these cases the person who has been dumped has a good track record of being emotionally supportive in an intimate way within that relationship. The person that has been dumped suits that role well.
Hope this sheds some light on that behavior. My advice? Always know your motivations, be straightforward, honest and open with the other person. Yes breaking up will still hurt and hurt a lot at times, but don’t muddy the water further.