Are there any examples in canon that show Dumbledore attending to the welfare of a Hogwarts student in as caring a way as he looked after Harry and, covertly, Draco Malfoy?
I almost want to include Tom Riddle Jr on the list above, as well, but Dumbledore didn't keep an eye on Tom Riddle out of altruism. Dumbledore was suspicious of Tom Riddle's psychopathy, and kept a close watch on Riddle accordingly.
Are there any other students¹ Dumbledore reached out to, or did he leave that to the Heads of Houses? If indeed he did show concern and caring towards another student, how did he demonstrate this?
★ I do not prefer an answer from the HP Wikia or the Wikipedia.
¹Students from any era during which Dumbledore was Headmaster of Hogwarts are eligible for any answer to this question.