there are ways, subtle, and not so much so, to let the less secure know that they cannot feel safe experiencing a full range of emotions around you.
some are more obvious, like mocking or yelling at them, but others are more common, more universally accepted, and just as clear
1. remind them of their past: there is nothing like clearing that moment of sadness or frustration or embarrassment only to be reminded of it, again, and again. nothing will encourage someone not to lose it around you faster than being certain to remind them that the incident is present in your thoughts and encourage ongoing judgement
2. ignore the reaction, notably: tuning someone out, as they escalate, is a sure way to clarify that this is an emotion you are not comfortable with. you don't want to encourage it, you don't want to wade in those depths, and you certainly don't want to work on it with them. trying to bottle an emotion in another? this is a sure fire way to go.
3. comment, without encouraging words: Hard day huh? How awkward! Seriously, the irony is that acknowledging, in a way that lacks empathy, a bad moment can be just as direct a message as ignoring the emotion. Want to make it worse? Add a dose of annoyance. Nothing will remind a human to mask their emotions more quickly than another human pointing out that they are weak, and have no sympathy for that reality
4. denying them that emotion: almost as bad as ignoring, and possibly as bad as mocking, is the moment in which you acknowledge a bad feeling and let another know that they do not have a right to react as such? the mild version of this is the "bright side" or silver lining. The more extreme is implying that someone is somehow negative or ungrateful or has some sort of disorder or perspective problem because they are reacting to something you don't think is worth that reaction.
So what can you do? How do you make a person feel safe to work through hard times and sad thoughts? At the very least, acknowledge kindly? Can't relate, don't feel safe or comfortable diving deeper: just let them know you hear them, don't have those feelings, but can respect that they can, and if you can't listen further, suggest options if that is what they need.
Even better, validate the emotion, share, if you can, a time you felt the same. Give them a hug, or even just let them be near you feeling that these are feelings they can face head on and work on directly.
Do everything you can to discourage shame, because shame helps no one.
Look, no one wants to be a downer. No one wants to be that person. You know, THAT person, who can't handle their shit, who is always sad or freaking out or acting out. Really. Or, at least the majority of people without severe personality disorders, just want to be thought of fondly. They aren't trying to upset you in order to win a sum gain.
The ugly part of this is: often in order to be holistically, we need all need to be that person from time to time. And whether it is death or destruction or just a bad day at the office that is calling up those feelings, we all deserve to feel safe having those feelings in order to figure out how to address them.
So next time you notice someone going there...going deep down there, consider your reaction. The smallest attempt to allow them to feel safe can make all the difference.