You question is not too clear, but in general if you put your name on the list in court and then leave before your case is addressed by the Judge, then you could have a bench warrant sent for your arrest. Even if your name is on a list, if the purpose of the court date was not completed before you left that could be considered a failure to appear. It really depends on the jurisdiction you are referring to, but I would consult a local attorney to check into your case.
Assuming you mean what happens if someone checks in and does not return, the judge will typically pass the case to the end of the call. If no one shows up, some judges will dismiss the case for want of prosecution. If you are referring to when an attorney or litigant checks in and then leaves to go to another court room, the case will usually get passed for a reasonable period of time until such time as they return to the courtroom.
Assuming you mean check in with the clerk, then leave before your case is addressed, it would be up to the court. The judge has the option of either issuing an arrest warrant, or forfeiting your bail bond and sending you notice that you must appear on another date. To be sure, you should call the clerk where you had court to find out the status of your case.
The answer depends on the type of case. If it's a criminal offense, a warrant will be issued for your arrest. For traffic, a judgment of conviction will be entered, with fines and costs, resulting in the suspension of your driver's license unil the judgemnt is vacated or paid.