If my son has a restitution order but has not paid anything in a year and has an upcoming court date, what can happen?
The court has a variety of options. The first is revocation of his probation. If the restitution was a condition of his probation and he failed to comply, then the judge has a basis for the revocation-- which means whatever sentence the judge was originally considering could take effect.
If the court feels that your son just needs a wake up call, then the court can simply sanction your son and order him to spend a few days in jail -- mainly so he would get a feel of what a longer sentence would be like.
Some jurisdictions have restitution programs where defendants are ordered to go work at a facility in order to get credits towards this restitution-- but this is not an option available in all jurisdictions.
If your son can prove that he had absolutely no funds available to pay restitution, then your son needs to raise indigency as a defense. If he doesn't have any attorney, he needs to request a court appointed attorney to help him with this option.