I dont know if thats something lots of people do, I'm only able to answer for myself. I could say that different people will have different reactions to arguments, and they can also have different reactions to arguments depending on who they are arguing with.
For Example-Crying after an argument:
If someone is arguing with someone close to them(emotional and relationship-wise) they might feel frustrated after arguing, and that may cause them to cry. Or they might feel sad or hurt and that may cause them to cry.
If that ↑ same person is arguing with a stranger, they might be less likely to cry because there is no emotion bond and may not even be all that affected by the exchange.
So, some may cry and others may not. Again, I am only able to speak for myself.
For me, when arguing with someone close to me, I sometimes end up crying way long afterwards because I'm not a confrontational person, and I tend to shut down almost immediately if I feel there's any sort of aggressive or accusatory tone, or that its somehow escalating- I absolutely stop talking about whatever it is the other person wants to argue about and my go to response is "Okay." and freezing. Sometimes I space out but that hasn't happened for awhile.
I cry afterwards because I'm frustrated at myself, then angry at myself and then guilty for shutting down. It might be a control thing or something.