Tomura Shigaraki has become one of the most dangerous villains in all of My Hero Academia. There are two major contributing factors to this. One is the grooming of All For One, the other most dangerous villain in MHA; he raised Shigaraki to be his successor and even passed down his Quirk. The other contributing factor is Shigaraki's destructive Quirk Decay; he has the power and desire to reduce everything he touches to dust. The combination of these two factors made Shigaraki a nightmare for Pro Heroes the world over, but perhaps they're not as separate as people think.
It's possible that All For One is personally responsible for bestowing the Decay Quirk upon Tenko Shimura, the boy who grew up to be Tomura Shigaraki. There are a number of aspects of the MHA narrative to suggest this. However, since nothing has been confirmed yet, many fans have come up with arguments for and against this claim. However, that doesn't mean that the potential evidence for and against the theory isn't fascinating to ponder.
The first thing worth noting is that Tenko Shimura started off without any Quirks to speak of. Normally, a person with a Quirk Factor will show it by the time they reach the age of five; if they don't develop a Quirk by then, it's likely they never will. This was revealed to be the case for Tenko in Chapter 235, "Tenko Shimura: Origin." If Tenko really wasn't expected to develop a Quirk of his own, then it's possible that he had Decay instilled in him.
However, there was a sign that Tenko developed Decay on his own; it just wasn't an obvious one. He had developed this terrible itch when he was a child, which was associated with some unknown allergy. In Chapter 236, "Tenko Shimura: Origin, Part 2," he was able to satisfy this itch by decaying his abusive, neglectful family. It's generally assumed that the so-called allergy was actually Tenko's destructive urges brought about by Decay. Since these urges had apparently been a chronic issue, it seems more likely that Tenko developed Decay himself.
Another hint that it was All For One who gave Tenko Decay was at the start of Chapter 235. The flashback in this chapter begins with a man escorting Tenko home after he was causing trouble with Hero-related antics. This stranger didn't have a name, and his face was obscured, but that leaves them entirely open to interpretation. It's possible that this man was actually All For One. If the man who escorted Tenko home really was AFO, then this might have been around the time he instilled Decay into Tenko.
As for why AFO would take an interest in Tenko in particular, there's an obvious reason. Tenko is the grandson of Nana Shimura, a previous holder of One For All and AFO's former arch-enemy. Corrupting her grandson and turning him into his successor would be a twisted way to stain her legacy and mess with her own successor, All Might.
More importantly, AFO giving Tenko Decay ties in with everything else he's done for the boy. He's canonically taken in the orphaned Tenko, given him the name Tomura Shigaraki, taught him everything he needed to be a good villain, and entrusted his villainous empire to him. He even passed his own Quirk down to the boy. It's clear that he had a lot riding on Tenko.
Of course, being the grandson of Nana Shimura wasn't enough. If AFO didn't give Tenko Decay, then he would have to rely on a lot of things lining up and working out in his favor. He would have needed Tenko to develop a powerful, destructive Quirk, kill his family, wander the streets as an orphan, and develop resentment for mankind; this would all have to be on top of Tenko being related to AFO's nemesis. For how carefully AFO likes to plan everything, there's no way he would leave all of this up to chance. Conversely, it would be just like him to plan everything about Tenko's life ahead of time, including his origin story.
The idea that AFO planned everything from the start is further suggested by more things that would otherwise just be coincidences. For one thing, he would have to have known where Tenko was wandering the streets and gotten to him before any of the Pro Heroes could. It also seems unlikely that he would have taken possession of the severed hands of Tenko's dead family if he hadn't somehow known precisely what happened to them; if he didn't, then they would just be another set of hands to him. These canonical plot points suggest that All For One knew far more about Tenko's situation than he was letting on.
Of course, there is something about AFO being behind everything that can come off as a cheap plot twist. While he's infamous for plotting everything far ahead of time, it would detract from Tenko's character arc and remove any sense of agency from the boy. It would carry far more meaning if Tenko developed Decay himself and killed his own family. AFO could still be responsible for everything else regarding Tenko's rise to villainy afterward, and the boy could still be held accountable for his own actions.
There may also be a condition revolving around AFO's transferral of Quirks that hasn't been met. Chapter 193, "Vestiges," seems to suggest that when AFO transfers a Quirk, it immediately manifests in the recipient. Thus, if AFO really is the man who escorted Tenko home and gave him Decay along the way, then it should have been immediately obvious. However, Tenko didn't decay anything until long after this interaction, which would mean that the two events are separate. Again, even if his "allergies" were an initial sign, he had apparently been suffering from them long before he met this stranger. The timelines simply don't match up well enough for all of these things to go together.
For now, AFO giving Tenko Decay is still just a theory. While many aspects of the story can be interpreted as signs pointing to this being true, it's still only speculation on the part of the fans. More concrete evidence needs to be presented by the narrative before any definitive conclusions can be reached.