In real life, this is known as Catatonia, and is common in a variety of mental illnesses such as Major Depression, Schizophrenia, Post-Traumatic Stress Disorder, Bipolar, and addiction.
People with autism spectrum disorders can "shut down" if overwhelmed (for example, by unexpected events or sensory overload). Depending on the person, a shutdown can be anything from staring into space with a zoned-out look, curling up and crying, or even a meltdown. More than one autistic person has been known to call their shutdowns a "mental blue-screen".
Everyone's had (or will have) at least one, some worse than others.
Slight subversion: Terry Pratchett went into "a frighteningly coherent rage" after finding out he had early-onset Alzheimer's disease.
... but he's left 'staring at walls' after receiving letters from terminally ill readers who state that they wish Real LifeDeath is the same as the one from Discworld.
Post WWII-Germany. It didn't really help that on top of everything, they were divided into 4 separate areas, and only 3 of those were shortly reunited.
After 9/11, George W. Bush had one on camera, sitting in a classroom, reading a book to children, when one of his aides came over and whispered what was happening into his ear. No matter what you think of the guy, you have to feel bad for him in the moment.
Most people in the US and arguably quite a bit of the world (since it was pretty much a wake-up call that "security measures" don't add up to a hill of beans and Anyone Can Die) probably had a bit of a Heroic BSOD moment/day on 9/11, and during various other large-scale attacks that have happened since.
The bombing of Pearl Harbor. Pretty much any national crisis will do, really (Tsunamis in SE Asia, massive earthquakes in San Francisco, Hurricane Katrina, etc.).
Southeast Asian and South American cultures (namely, the people from the Amazons and the Andes zones) have terms for this which anthropologists often translate as "soul loss". Souls can wander around temporarily outside their bodies for many reasons, not all of them detrimental, but if your soul is blown out by a sudden shock or extreme fear or anger — your own, or someone else's directed at you — it might find itself in unfamiliar space, unable to get back in. This can cause serious illness. One of the specialties of traditional shamans is the recovery of lost souls.
In Mexico, the condition is called susto. Similar beliefs exist in other world cultures including Taoism and Shinto.
According to Eve Curie, her mother Marie had one of these after the horrific death of her husband and fellow scientist Pierre (he slipped while crossing the streets under the rain, was hit and run on by a horse carriage, died of a terrible skull fracture). She was helped by her sister Bronya (a doctor), and by throwing herself into hard work. Most of this is admirably portrayed by Greer Garson in the film version of Madame Curie. Less well known is the fact that Marie and Pierre both believed in Spiritualism, so Marie may have been comforted by the idea that she could go on communicating with Pierre in the next life.
Phil Collins admitted to having one of these during the breakup of his first marriage.
Brazilian footballer Ronaldo suffered a convulsion in the day of the 1998 FIFA World Cup final. What exactly happened is unclear to date (and subject to Epileptic Trees), but affected him - who still decided to play the match - and Brazil's team, who proceeded to lose to France 3-0.
This is a major symptom of PTSD, and is usually life altering in its effects.
The United States' National Weather Service suffered one of these during the 1974 Super Tornado Outbreak, with the technology they had at the time, there was no way they could handle 148 tornadoes in one day, so many warnings were issued that it overwhelmed the system
Supposedly Josef Stalin had a major one of these after finding out Germany had attacked the USSR. At first, he refused to even believe such a thing was true, until he had overwhelming evidence to prove that yes, Russia was under attack.
Lázaro Cárdenas, former president of Mexico, had one of these when he found out the Mexican Army was used to kill innocent people (as someone would later quote "he couldn't believe the army created in the Revolution would be used to kill the Mexican People itself").
Whether he's heroic or not is a matter of debate, but boxer Oliver McCall suffered a blue screen of death during his second fight with Lennox Lewis. Apparently a punch dislodged the part of his brain that was keeping him from thinking about his legal troubles and clinical depression, and he simply stopped fighting or defending himself, then went back to his corner and cried until the ref called the match.
Ozzy Osbourne has suffered at least four or five: One when he was fired from Black Sabbath, another when his Heterosexual Life Partner Randy Rhoads died, another when he was mistakenly labeled as HIV positive (in the 80s this was a death sentence, and it turned out all the drugs and booze he was consuming made his immune system just stop working), yet another when his wife Sharon was correctly diagnosed with colon cancer (again, he assumed it to be a death sentence), and an arguable one when his mother passed away. Poor guy.
Elton John seemed to have one beginning in 1987, when dealing with potentially career-threatening vocal problems which required surgery (it deepened his voice to the point his falsetto range was reduced or disappeared); he was dealing with nasty untrue headlines written by British tabloids (he sued them and won), and his heterosexual marriage to Renata Blauel collapsed. All while Elton was heavily involved in drugs, alcohol, bulimia and depression at the time.
Both Elton and his main lyricist Bernie Taupin suffered one around 1976, due to burnout from fame and touring, cocaine and alcoholism on both parts, backlash due to Elton proclaiming himself bisexual, and Bernie's first marriage collapsing. This led to the somber tone throughout Elton's 1976 double album Blue Moves.
The city of Liverpool went into a collective Heroic BSOD when the Hillsborough Disaster happened. Everton and Liverpool fans alike went into mourning; many had friends or family who died. The anger and grief felt throughout the city because of Hillsborough was so great that when the Sun printed lies about Liverpool fans robbing and urinating on corpses, sales of the paper dropped on Merseyside due to boycotts, and have never recovered since. In fact, it is not only not bought, but actively campaigned against, and almost no newsagent carries it.
Invoked in the memoir One Bullet Away: The Making of a Marine Officer. Then Lt. Fick was secretly ordered to fake a Heroic BSOD during a training exercise to test the current squad leader. After several days of being yelled at by his friends, Fick eventually revealed it was a ruse.
When the news was let out that FDR died, and that MLK, Jr and JFK were assassinated, many people experienced it, and many authors have written about the social affect and effect.
Captain Edward J. Smith, commander of the ill-fated RMS Titanic, supposedly fell into a near catatonic stupor when he realized that his ship was going down in the middle of the Atlantic. He was only briefly brought out of it by his second officer shouting at him and asking if they should order the women and children into the lifeboats.
Ulysses S. Grant went through one and went through it hard during Abraham Lincoln's funeral, where he wept profusely. He was supposed to go to Ford's Theatre with Lincoln but had to change his plans at the last minute. Grant always said that, if he was there, he would have heard the assassin coming and stopped him before Lincoln was shot. After the funeral, Grant said that Lincoln was the greatest manhe ever knew.
Rather infamously in the case of Herbert Morrison, trope namer for Oh, the Humanity!. He became so horrified during the report of the disaster that made him famous that he became a sobbing, incoherent mess for a few seconds, before he finally had to walk away from what he was seeing. He recovered within minutes and continued to report on the firefighting and rescue attempts afterwards.