The fine will accumulate as a result of any more scans of nefarious acts in the next 7 days (from the time of the first fine). Nothing will happen to you during this time in the system that gave you the fine.
After 7 days total, the fine becomes a bounty. You will be Wanted in this system, but not others. But your bounty will show if someone does a full KWS on you. Not very much will happen to you; in the system that gave you the fine if you are scanned by NPC security they will attack.
After another 7 days, it becomes a legacy fine and can be completely ignored. Or paid off, if you're feeling plush. Any further fine-inducing activity in the system will re-enable the fine back to its original level.
If you die, the fine will need to be paid off and added to your rebuy costs.
If you're wondering why a player who is caught smuggling faces a fine over 150 times bigger than a player who is caught murdering, keep wondering, it's a mystery to me too.