This is a bit like asking "what would happen if someone takes a plea deal to go to prison for x years and then just doesn't go?"
Plea bargains don't include any voluntary agreements to do or not do something, precisely because they could not be legally enforced without violating the double-jeopardy rule. A plea bargain means that the defendant will plead guilty, and in exchange receive a conviction from the court with no more than the legal punishments they agreed to.
One of those agreed upon punishments might bar them from running for a public office. Which is then part of the sentencing. It means that they don't have to promise to not run for office, they are legally prohibited from doing so. Which means it would not be allowed for any voting commission to put their name on the ballot, and any write-in vote cast in their name would be invalid.
However, a court might not be legally allowed to inflict any punishment it wants. For example, the criminal law might not allow them to punish a defendant by revoking their passive election rights. In that case, such punishments are usually implemented through a probation clause. For example, the defendant receives a prison sentence for x years on probation, and that probation has a term that the defendant must not run for a public office for y years. If they do, then they would have violated their probation terms. Which means that they would have to go to prison for x years.