I've had these reactions come up more than a few times over the years. Nearly always with a brand-new beginner (first few classes, or at a seminar). Some are as subtle as you mention, and others are breakdowns. As for suddenly not coming to class - can't really say how often that's due to one of these situations, as students do that all the time, for more reasons than I can fathom.
When it happens during a class - assuming they don't have a support person there (spouse or close friend - that changes the dynamic), I normally would ask someone else to watch the class for a bit and check to see if she (yes, as you indicate, this is normally a woman) is doing okay. If she can continue, I'll watch what's immediately causing the reaction, and look for a way to temper it (if it's a touch to the neck/throat, I'll shift the contact point, which often helps). If she's struggling more than that, I'll ask if she needs to sit down for a minute, try to get her away from the class without drawing too much attention (it's a futile attempt - always draws attention, anyway). And I'll ask again if she's okay. Some of them want to talk a little about it (usually no more than "something happened a long time ago" or "I was attacked that way once" or something else suitably vague. If she wants to talk, I just let her. If she wants to step back on the mats, I ask if she wants to try the same exercise, change it a bit, or work on something else - I let her choose her level of comfort.
Unfortunately, I'm neither trained nor equipped to do much beyond that in that situation. I have some training from long ago in crisis intervention, which has helped me help some people close to me, but none of it was training for these kinds of issues. If I had someone who seemed to need help (and who stayed long enough for me to offer contacts - none has yet - the ones that were that heavily stressed just left and I never saw them again), I'd offer to give her the number of a local service that can connect her with someone capable of offering help.