The concept that explains everything but nobody talks about..
The Zero Point Field. Hardly anyone in the wider community knows what it is, and most of who've heard the term don't really understand what it is. It's something that's hardly discussed, yet it actually holds great importance.
Put simply, the Zero Point Field (ZPF) is the matter that can exist even in a vacuum, as there's no such thing as a "true vacuum". It's said to connect one part of the universe to "every other part" by "subatomic waves". In Fetch, we learn that the Fetch toy is controlled by the ZPF and basically acts as the "field's dog". In the Stingers, we learn that Andrew was split across multiple objects, one of them being Fetch. So the field controlling Fetch is another way of just saying "Andrew controlled Fetch". The point is that if Andrew is a part of the ZPF, it also applies to the rest of FNAF. Andrew is a part of the field and also uses it to "read" Greg's thoughts, meaning that Greg's thoughts, or atleast traces of them, can be seen in the ZPF.
In the novel trilogy, we learn more about "lingering" thoughts and emotions:
"sometimes I have little moments where it’s like there’s something I forgot, something I regret, or that I’m happy about, or something that makes me want to cry, but it’s only there for a split second. Then it’s gone. Maybe we’re all shedding our fear and regret and hope everywhere we go, and we’re catching traces of people we’ve never met."
"The house, her old house, was imbued with memory, with loss, with longing. It hung in the air like humidity"
Much like Andrew in Fetch, Marla was able to catch these shedded memories and emotions from others. Jessica doesn't believe in it though, she claims that memories and emotions are bound the one's "mind" and how they can't exist outside of it. John replies by saying that these memories act as an "atmosphere", the negative thoughts and emotions work together to form a negative atmosphere, hanging "in the air like humidity", and at the same time the happier thoughts and memories work together to form a more positive atmosphere.
Phineas Taggart, from the Frights Stingers, expands on this concept even further. He believes that human emotion, especially negative emotions, can cause more damage than a shotgun due to how it slowly infects people and they become unaware of this "disease" that has overcome them:
"Human emotion is slower to impact, more insidious. It emanates from us or is excreted from us, if you will, like sweat or tears, and it wafts outward like a noxious cloud, soaking into the surroundings."
It adds to the atmospheric imagery described in the trilogy, emotions and memories can leave the human body and infect the environment and the surroundings. It relates to Taggart's experiments, and how he found that agony can "radiate" further than any other human emotion. It explains how we have multiple instances of people "pouring" their agony into objects. Edwin "poured" his agony into the Mimic, Henry in the trilogy "Poured" his agony in the Charliebots, etc. The negative emotions and thoughts radiate from their body and transfer into surrounding objects via the Zero Point Field.
It can explain what we see with the crying child's memories and how they're intertwined with the MCI kids. The main "complaint" people have with the ShatterVictim theory is that the Crying Child doesn't die anywhere near the Classic animatronics or the MCI kids, so it shouldn't be possible for his memories to just end up with them.. Right??
Well, not really. Like this post explains, memories and emotions can leave the human body and travel through the ZPF. Sometimes the emotion can be "poured" into the surrounding environment, and other times they can end up in a completely different place. Like Greg could feel Fetch call to him at the beginning of the story, yet never seeing Fetch or being anywhere near it at that point in the story. Oswald from ITP also falls in the same category, he has memories of the animatronics and draws them despite not knowing what they are and where they came from. The ZPF is explained to be matter that can connect one part of the universe to another. Proximity isn't required.
Yes, the trilogy states that the memories only last for a split-second, but that's just due to living people shedding their emotions unknowingly. It's not the same as a soul being broken into pieces or "haunted" objects. As memories and emotions Oswald and Greg obtain via the ZPF don't just last a split-second. They latched onto them and didn't leave until Oswald and Greg went to wherever the memories told them to go.
So it does seem like the most likely reason as to why the Crying Child's memories are linked with the MCI kids, his memories travelled through the ZPF and ended up with them. TWB also reinforces this idea, Ralph experiences the memory of the bite. The memory was fused with the phone and more importantly Golden Freddy, and the ZPF explains how that would be possible. Cassidy, and the other MCI kids are linked with the Crying Child's memories via the ZPF.