This sounds like absolute heaven.  

I don't tend to do this, but I'll say that I often cry with other people simply because I'm usually also involved in whatever is making them cry.  To be honest, I have a completely different set of issues.  When a guy is crying (or, more commonly, when I think a guy MIGHT be crying/about to cry) my heartbeat tends to quicken.  I guess it's sort of like a "whoa, this is it!" moment, since guys crying (mine, in particular) is such a big deal to me and something I fantasize about so frequently.  I tend to worry about that, because I'm afraid that the time will finally come to get to hold my boyfriend while he cries and he'll feel my heart pounding and get really weirded out by me.  

I'm very similar.  I'm pansexual, but I, too, am turned on very primarily by male tears, and I think it is for the same reason.  Girls are often much more comfortable with crying because it's publicly accepted, whereas with guys, it's a huge deal to them.  

I have had a few fantasies with women, though. Primarily, the woman has been abused in some way (not always in a sexual way or by a romantic partner, but just in general) and is staying at my house for refuge.  She's so scared that she needs to sleep in my bed and I hold her crying form all night to help her feel safe.  Sometimes, she also has issues with feeling worthless, and we end up making out while she cries, me trying to show her she's loved.  I think my brain needs all these extra levels of complication to the story when it's women in order to make them feel more vulnerable and put them more on the level that men start out on anytime they open up like that.

            They stepped into his apartment, and she studied his face, waiting for signs of recognition to flicker across his features.  None came.  He looked around curiously, as though he’d never been here before in his life.  She withheld her sigh.  She had been listing everything she knew about him since she’d picked him up from the hospital, but nothing had helped jog his memory.  It terrified her to think that amnesia could hit anybody at any time.  After all, the doctors had found no signs of head trauma. 
            “So, I live here?” he asked as he began to explore.
            “Yep.”  She followed him around, pointing out various knick-knacks and explaining their significance to him.  He remembered a few things here and there, but they had all been with him for most of his life.  No new breakthroughs seemed to come.
            After a while, she noticed his attention start to fade.  It had been a long day, and she must have overloaded him with information by now.
            “Why don’t you go to bed,” she suggested.  “Maybe you’ll remember more in the morning.”
            He looked at her, then turned his head toward the door.  He bit his lip.  “Do you think, maybe, you could…stay?”  His voice dropped to a little above a whisper.  “I don’t want to be alone, right now.”
            Her eyes softened.  “Of course.” 
            She followed him to the bedroom out of habit, but she stopped herself when she reached the doorway.   “Oh.  I can stay out on the couch, if you want,” she suggested, jerking a thumb in the direction of the living room. 
            He studied her cautiously for a moment.  “I guess you normally stay in here with me, huh?”
            “Yeah, but it’s no big deal.  I don’t want to make you uncomfortable.”  She tried to force her voice to stay positive

I love your ad!  I just don't know how one would go about finding something like that. It would be nice if people like us were more common; we could just make a support group/network for each other so that when one of us did need a shoulder to cry on, we could contact someone else who would be there for us and also appreciate the opportunity lol.  I do envy the BDSM community for that; it must be nice to be into something so common that groups are formed around it.

One idea I had for a search term was hurt/comfort, because I know there are a lot of people into that in the fanfiction world, so I thought maybe someone might have thought to make a "real life hurt/comfort group" or something like that, but I didn't see anything. I feel like we live in a world where this is doable, but the challenge would be difficult to overcome, especially as someone who would rather not announce this to everyone I know.