What happens if one has a PhD scholarship and drops out in the second year of the PhD program? Should he pay back the money that he got in his first doctoral year?
This will depend on many things including local law and the details of anything signed. In the absence of some rule, it is unlikely that there is any need to repay. In particular, many funding agencies have no real way to accept money paid back. The reason that the person dropped out may be very complex, and actually a shared issue with the institution.
But this can differ widely. Read the fine print if any.
In the scholarship agreement of the UK research-intensive university in which I work, there are no conditions under which the recipient will be required to pay back tuition support. The only provision that comes close is a clause for suspension of stipends (as opposed to the tuition component) if the recipient fails to demonstrate appropriate academic progress. (What many don't know is that a formal finding inappropriate academic progress often takes up to 12 months to weave its way through the university bureaucracy, so the termination of the stipend can take a while to take effect.)
In the case of a staff member undertaking a part-time PhD, there is such a clause. Eligible staff are awarded a tuition waiver to undertake a part-time PhD. Those that take this up are required to work at the university for a specific amount of time. The clause to which I refer states that if employment is terminated prior to the work requirement is fulfilled, the University may seek to recoup the tuition waiver. I have never seen this clause enacted.
The effect of a termination of studies has an effect on the supervisor, too. The scholarship policy states that terminations or withdrawals within the first six months of candidature means that the supervisor may choose to reopen the search for a scholar. If the termination or withdrawal occurs after six months, then there is no chance for the supervisor to do this and the scholarship opportunity is cancelled by the Graduate School.
I hope this information helps. Good luck.