Work (hopefully) doesn't consume our entire lives. Every single one of us comes from a different background and we're also all in very different stages. Despite this obvious fact, there's still a ridiculous stigma against people expressing emotions at work. We aren't robots, so what's the deal?
Let's first think about what people consider "emotional" behavior based on gender biases—I think it's important. If someone says a woman is being emotional at work, they might think she's angry or aggressive when disagreeing with a statement or correcting someone if they interrupt her. These same people think this is normal behavior for men and don't call them emotional for it. Come to think of it, do men ever degradingly get called emotional for any of their behavior at work? I've never seen it in my own personal experiences.
But what if we all could show some emotions at work without it being seen as a bad thing? Our jobs are frustrating. Software is frustrating. Clients are frustrating. So what if someone gets mad at their desk for 30 seconds because the bug they've been working on for a few days or a week is still not fixed? As long as they aren't being disruptive to their teammates, I don't see a problem.
If someone is going through something in their personal life, such as losing a loved one, let them have some space when for a while. They're probably going to be really quiet for a few days. They might cry at their desk or hide in the bathroom. If you see them do either, just be supportive. It's not hard and it doesn't have to be awkward. Also, keep it to yourself if they confide in you. It's not your place to chit-chat about someone else's situation.
So, let's normalize people being human at work. I get that it's a society-wide issue, but I can't think of a better place to start fixing it than at your work, with people you interact with on a daily basis.