The last time we see Monks in the story is in Chapter 51. In this chapter Oliver learns that Monks is his half-brother, and Monks admits that he destroyed their father's will because their father left most of his fortune to Oliver, and relatively little of it to Monks. In a characteristic act of benevolence, Oliver nonetheless agrees to give half of his father's fortune to Monks, so as to give Monks a second chance.
At the end of the novel, in Chapter 53, we learn that Monks fled with his fortune to "the New World," where he promptly "squandered it" and "fell into his old courses." The implication here is that Monks once again became involved in criminality. We are told a little later that he committed new acts of "fraud and knavery" and that he was put in prison. The last we hear of Monks is that he died alone, in his prison cell far from home.
Monks's story is a sad one, especially because of the way it ends. The fact that he succumbs again to criminality at the end of the story shows that criminal behavior is linked not only to extreme poverty, but also to neglect. Indeed we discover earlier in the story that Monks was neglected and mistreated by his mother when he was a child, and this mistreatment seems to affect him for the rest of his life. Just as Oliver is unable to escape his poverty, Monks is unable to escape his upbringing.