The person you are talking about is Caleb Phipps, he appeared as an Irrelevant Number in the 11th episode of the 2nd season (2πR).
When we first meet Caleb, he is a teenager, who performs poorly at school. He also anoonymously deals drugs to support his mother who become an alcoholic after Ryan's (Caleb's brother) death. Ryan was hit by a train while the brothers were drunk and crossing tracks on a dare.
Finch poses as a substitute math teacher and quickly realizes that Caleb is in fact a computer genius, working on a revolutionary compression algorithm named 17-6-21. This turns out to be the exact age Ryan was when he died and Caleb's current age. Finch figures out what Caleb's about to do - he is blaming himself for Ryan's death and wants to commit a suicide in the same way his brother died.
Finch finds Caleb at the train station and sits down next to him and manages to convince Caleb not to kill himself.
The next day They meet outside the school. Finch warns Caleb to be more careful with his code and tells him a story of a young hacker who changed everything with a home-made PC in the early days of the internet.
As I see it: Finch saved Caleb from himself and gave him reason to live.