Short answer is that the obligation to pay the fines never goes away. The long answer is that not all of the processes that the court usually uses to get people to pay fines (i.e. contempt and revocation of probation) may be available to the court. The court cannot likely revoke your probation if it is outside the normal term of probation for a misdemeanor, which is 2 years, or 5 years for a felony, but this term can be extended in order to complete restitution AKA payments to the victim. There is nothing in the statute, KRS 533.020 authorizing extension of probation for payment of fines. Therefore, this means the court could not likely impose your original sentence if it is outside 2 years for a misdemeanor conviction or 5 years for a felony conviction.
However, the court can still use its contempt powers to make you pay the fine but there is process that goes along with that. Simply put, if you are ordered by the court to pay fines and you don’t then you are disobeying the court’s order. Judges expect their orders to be obeyed. If the orders are not obeyed then the judge can impose punishments up to and including jail time. However, before imposing those punishments for financial related obligations, the court must make a specific finding of fact upon his or her ability to pay and any further contempt proceedings should be limited to those amounts which the person is found to be able to pay. Also, if jail time is a possibility then the person has a right to appointed counsel AKA a public defender.