This, among a few others such as uncontrolled monopolies, are the few failings of a completely libertarian society.
Government ought to have an umpire role, not a player role. It is to help in minimising the failures of markets: externalities and monopolies. But just because there are externalities in energy, or monopolies in transport, it doesn't mean the government should necessarily be the key player in those industries. They should merely be the referees, setting up appropriate law and order to provide the necessary incentives for a market mechanism to do the job properly.
A bit welfare would ensure this person will get back on track and contribute to society again. However, there is the true consideration that the government ought to not take my money forcefully (through taxes).
In this sort of situation, I believe the government's role is to act only as a facilitator - to create the means for those able and willing to contribute to welfare to do so. Perhaps an opt-in system to take a bit more tax for this very purpose?
Private loans would do, if there was
really so much potential to be unlocked in these people.