So, I'm actually not a big crier, so I don't really have an answer for this one. But, I do want to share something I learned about when I was becoming a teacher.
When people are upset, crying, in flight or fight mode, they're in a part of their brain I learned as the "lizard brain". This part of your brain is what determines if you should fight or flight, and once someone is in that part of their brain, higher functioning becomes near impossible. So, how do you deal with this? Well, the answer we were given for kids also works really well for adults because, get this, kids are people too. Anyways, the biggest thing is get moving. Walking, biking, running, literally anything that involves movement. This will start using up the adrenaline your body is pumping (I'm not a biologist so if I'm describing this wrong I apologize) and slowly get you out of the lizard brain and into your higher functioning brain where you can articulate what's wrong and calm down. It is amazing how much someone who is closed off and angry will start opening up once they've been walking for a bit, and allowed to just think through their feelings.
Number 2 is change the scenery. This kind of happens once you start moving but if going for a walk or something isn't an option, simply changing location (to another room for example) can do some amazing things for the brain. It's kind of stupid how simple the brain is at times, but something as small as just changing a location can help get the brain to go "wait... this isn't where we were crying... It must not be crying time" lmao
A story about this: When I was with my ex I came home from a long day of school and work, and she was really upset about something. Very anxious and pretty much crying or on the verge of tears for most of the day. So, I went inside to my apartment to get her, told her we were going for a drive. And we literally just drove around for a while. And sure enough, after some time, the anxiety passed and she was able to calm down and work through some things. I also have used this trick a couple of times on friends who sort of curled up in their depression balls in their room.
Obviously, I'm not saying this is the miracle cure that will get you out of the worst panic attacks or whatever. Also, it's obviously very hard to get someone who is in serious depression or anxiety to do something. But it can be a really useful tool to try to use on yourself or others if you or someone else is in their lizard brain mode.