I have no idea. It doesn't make sense to me. Where did you see that used?

Gary is correct. An unspent conviction is a term from the British criminal justice system. When convicted of a crime in court, that conviction will be unspent for a certain period of time (called the rehabilitation period), meaning that it remains against your personal record and must be declared whenever you are asked about criminal convictions when completing any legal document. The length of rehabilitation period (for how long the conviction is unspent) usually depends on the length of imprisonment – for example, prison sentences of more than two and half years will never become spent and most always be declared; prison sentences of more than six months but less than two and a half years, remain unspent for 10 years and a prison sentences of less than six months, remain unspent for 7 years. Once the rehabilitation period has passed, the conviction is called spent. However, there are certain convictions that must always be declared, whether or not these are spent. When applying to work with children, vulnerable adults or in the legal profession, you must declare all criminal convictions, even if they are spent, that is, even if the rehabilitation period has ended.

Ah. I just looked it up. It is a British phrase. I guess therefore ( and also based on the luddite nature of a University not having online forms 8^| ) that it is a British University? Over there - there is a rehabilitation period associated with a conviction. So - you do a crime, then perhaps get imprisoned, then some time after that, if you have not been convicted for something else, you no longer have to declare that conviction on certain applications.