Who is responsible for Tom Robinson's fate?

That is a very interesting question, and one that does not have an easy answer. For one thing, there are quite a few people in the story who can be held in some way accountable for what happens to Tom. First of all, there is Mayella Ewell, who makes what she knows full well is a totally false accusation of rape against Tom. Then there is her repulsive father, Bob, the instigator behind the phony accusation. He is tired of being a despised nobody in Maycomb; pointing the finger of blame at Tom allows him to act like a hero and pose as a defender of white womanhood's honor against the rapacious threat of savage black men.
Perhaps we could also look at the twelve jurors. They were so blinded by racial prejudice that they willfully ignored and overlooked the massive holes in the prosecution's case. They were only supposed to convict Tom if the prosecution established guilt beyond a reasonable doubt. However, because the case against Tom was so flimsy, it is obvious that there was more than just that involved.
Finally, there are the prison guards who shot Tom seventeen times as he tried to escape. They were immediately responsible for his death in that they fired the fatal shots. They did not really see Tom as a human being. To them, he was just a dangerous Negro criminal needing to be taken out.
In truth, though, Tom's tragic fate had been decided long before his actual death. Maybe we should not look so intently at the actions of individuals. Instead, we might like to concentrate on the systemic racism and prejudice that helped to create and shape those actions. This is not intended to absolve anyone from the shameful part they played in Tom's eventual demise, but by examining the wider context of how these people made their choices, we can gain a better understanding of why people often act as they do, in ways that most of us find completely unacceptable.