Punishment is logically (1) a penalty (fine, imprisonment, community service, &c.) (2) of an offender (3) for an offence, a crime committed. There is also (4) a requirement that the penalty be imposed by human agency - some natural diaster befalling the offender does not count as punishment - and (5) that the penalty be imposed by an authority of some kind, personal or institutional.
That the crime 'physically cannot be committed again', makes no difference: punishment occurs when conditions (1) - (5) are met. Punishment is for an offence, a crime, regardless of whether the crime can be committed again.
A reformative theory of punishment would still apply to the case you describe. There is punishment because the crime has been committed and the aim of reform would be to prevent the criminal from engaging in similar crimes or to discourage her/ him from law-breaking in future.
Reformation (successful or otherwise) of the offender does not replace punishment here; it is the aim of punishment or an accompaniment to punishment. Reform is punishment plus.
Reference
A. Flew, 'The Justification of Punishment', A Philosophy of Punishment, ed. H.B. Acton, London: Macmillan, 1969: 83-104.