After Frank nearly killed Billy and he had memory damage, he had forgotten the last few months. Which meant he forgot he had tried to kill Frank, how he tried to kill you, and all he remembered about you was how you two had been close since childhood. That’s all he knew.

So when he escaped the hospital and killed again, he went to you after. He didn’t know where else. He didn’t know how he knew where you were. Billy just knew. And he began staying with you, knowing he was a criminal.