Jesus looked steadily at him and loved him. This unnamed man is then given a special vocation. It is the same vocation as Matthew. He was called to be the thirteenth apostle. “There is one thing that you lack. Go and sell everything you own and give the money to the poor, and you will have treasure in heaven: then come and follow me”.
Note the following text. “But his face fell at these words and he went away sad, for he was a man of great wealth”. It is not Jesus who is sad. Jesus just gets on with the job and he will call others when he needs them. We hear no more about this man in the Gospel.
This leads to a lively discussion between Jesus and his disciples about riches. Jesus talks about the incompatibility of riches and the kingdom. The only solution is “For men it is impossible, but not for God: because everything is possible for God.”
The vocation of the rich young man is a special vocation akin to the vocation of St Francis or Mother Theresa. He clearly refused the invitation. We know no more from the Gospel. But from the Gospel we may be sure that Jesus does not give up on him. All of us are given another chance. “Everything is possible for God”. It is interesting to me that this man is honoured in one of the eastern liturgies as a canonised Saint. I can’t vouch for that, but it gives me hope.