Criminal punishment within the Republic is an odd beast, as for the most part it largely relies on rehabilitation or fines to deal it's non violent criminals. So, things like public drunkenness, jaywalking, petty theft, pickpocketing, and other crimes that do not harm a person but are considered to go against society's values. On the other hand, the Republic does use execution to deal with its more violent prisoners; such as murders, arsonists, rapists, terrorists and other crimes that see the serious bodily injury or death of a person.
The rehabilitation process of the Republic focuses on the idea of creating a better person, for this they need to be pulled away from their old setting and placed in a new and more productive setting. This setting is usually the prison colony in the system X-223 at the Victus Space Prison complex. Here they will be inducted into their rehabilitation program that teaches the applicants here new skills in ever demanding fields, such as mining, manufacturing, telecommunications, and so on. The idea is not to punish these offenders, as they usually do not have opportunities as others or they have just lost themselves and need some help getting back on track, instead it is to help them be better citizens of the Republic.
Mostly reserved for violent and aggressive offenders that are deemed to be a threat to society if released and have no chance at being rehabilitated. However, this can be used to deter certain highly immoral crimes as well, for example grave robbing, maltreatment of the deceased, and so on. These criminals are usually sent to the prison system known as X-659 and housed at the New Hope Space Prison complex where they await their execution. Execution within the Republic is usually done by one of two ways, firing squad or hanging. These two methods are deemed to be the most humane and effective measures of execution, not to mention they are incredibly cost effective. However, they do not simply wait in their cells for the dreadful day at the noose or by the gun, instead while they wait they are put to some limited work by mining out the asteroid that the space prison is located on. The idea is that they are already about to be deadmen, so maybe they can do the Republic some good by helping out with a bit of mining.
But this brief period of dread and waiting is usually short, about a week, then they are placed in the execution room. They will be read their rights, asked for any last words, and finally executed. Most of the time these executions are kept behind closed doors, with only family members of the victim and the executed attending them. On rare occasions, such as terrorists and serial killers, there will not be an audience to witness their execution.
However, there is one crime that is universally reviled by the Fenvarians, and that crime is treason. This crime is considered especially heinous, as it goes directly against many of the things that the fens believe in. For example it means you are betraying the relationship that you and society have created in order to survive, it also means betraying your family, and it means that you have failed in your duty as a citizen.
So the rational behind it, is that just as citizens have rights, they have duties and responsibilities as well. As the republic protects you, so too must you protect the Republic and the things that it stands for. This harkens back to the rather ancient times of the fenvarians where survival was important on their cold and harsh planet. Family and community bonds are held close and everyone relies on another to survive, and supplies are limited. In modern times, this has expanded to a sense of duty to protect the whole nation. While supplies are not limited as much anymore, the idea is still there. Since a traitor taking up space in a prison or rehab facility is taking up supplies that could be used elsewhere and there are really no redeeming qualities with that person since they have broken the trust with the Republic as a whole.
When it comes to punishment of a traitor the punishment is often swift and made to set an example. The traitor is usually hanged with a noose and then shot by a firing squad, after that they are then cremated and thrown into the sun. Usually Fenvarians are buried, however since they broke their bond and trust with the Republic it is believed that they cannot give back to the Republic in any way or form.