If you don't go for a fine, you will most likely just be charged the amount of the fine without a chance to contest. (For example, parking tickets give you the option to appear in court and argue why you believe you should not have to pay the fine. If you miss that court date, the won’t be any repercussions, you will simply loose the chance to have the fine expunged).
If the fine requires a court appearance, your fine amount will increase until you have met with the courts. If this goes on for long enough, it could result in an arrest.
If you miss court for a law suit hearing, you will charged for missing the date (which is typically a hefty fee). Depending on the severity of the law suit, you may be automaticity considered guilty, given a warning and a new scheduled court date, or put under arrest for failure to appear in court.
hopefully this helps. If you wish to include what the fine or lawsuit is in regards to, I could possibly give you more specific answers.
