The best quote from the end of Oliver Twist indicating that Oliver has survived all his misfortunes and adventures and misadventures is as follows:
Mr. Brownlow adopted Oliver as his son. Removing with him and the old housekeeper to within a mile of the parsonage-house, where his dear friends resided, he gratified the only remaining wish of Oliver's warm and earnest heart, and thus linked together a little society, whose condition approached as nearly to one of perfect happiness as can ever be known in this changing world.
This quote follows the narrator's description of Monks' fate. Mr. Brownlow advised Oliver that it would be fair and possibly advantageous to Monks if the inheritance left to Oliver by their father were divided between the two instead of going, as the will directed, solely to Oliver. Oliver joyfully agreed to the advised plan and Monks became the possessor of three thousand pounds. He left for Australia but the hopes for his new life there were dashed as he was again penniless, imprisoned, and soon dead.
Oliver's other friends Rose and Harry are married and move into a cottage for Harry's first parish as a clergyman. It is they to whom Mr. Brownlow and Oliver become neighbors, thus fulfilling Oliver's wish of being within distance of his dearest friends. He has survived and will thrive under good and loving care and guidance.