Irregular

Note: It is unknown who or what teleports them into the Tower or even how teleportation functions outside of the Tower. It is also unknown exactly what qualities are required to enter the Tower apart from possessing inner strength like determination, perseverance, bravery in the face of danger, etc.

'''Note: Uncontrary to theories floating on the forums and so on, there's no proof anyone has mentioned Irregulars have forced open the doors. '''Even Yuri Zahard mentioned that someone "opened the door"(Ch 2) and Yu Han Sung mentioned Zahard or Urek Mazino was "one who opened the door himself"(Ch 58).

Introduction
In the current political system, under the contract Zahard made with a Guardian like Headon, Headon visits the Outer Tower and outside the tower to select Regulars(Ch 10). In this system, Irregulars are called "unchosen Irregulars" and regulars are called "chosen Regulars" or "selected chosen"(,Ch 2).

Politically, Irregulars are viewed as beings who have entered the Tower and in turn, the Inner Tower, without being chosen by Headon. And according to Yuri Zahard, they're "probably not too welcome"(Ch 2) and she assumes Headon doesn't like Irregulars.

However, before the current testing system was established, the original testing system of the Tower was likely created for Irregulars and thus, they are the true chosen ones. In ancient times, the terms "Irregular" or "Regular" didn't exist. The Irregulars are the ones who open the door of the Tower themselves, according to the Guardian of the 2nd Floor(Ch 58). And likely, the term is a simplification of the entire process as one doesn't physically open the doors of the Tower to enter it.

Note: it is uncertain if the Tower was created solely for Irregulars alone as groups of people were living in there before Zahard's arrival.

A possible outline of how Irregulars are selected
People who live in the land(s) outside the Tower are selected by The Tower if they meet a certain criteria. It's unknown what other qualities are required other than "true bravery", "true perseverance", "certain combat qualities", "true determination", "extreme courage", "judgement"( for a person to become a "chosen one". This is evidenced by the fact Headon told Rachel that "you're not the person the Tower has selected" and "you have not been chosen"(Ch 76). Although it is possible Headon or another Guardian is involved in the choosing of an Irregular, it's likely the Tower does the choosing and possibly, even the teleporting.

Examples of Irregulars include Zahard and the 10 Great Warriors and Baam. They are then selected by the "light" of the teleporting system and then teleported through the doors of the Tower into the Tower itself. While they're being teleported through the doors, they're still physically present in their current location ( Ch 76).

The Guardian's tests
They are then teleported to the First Floor to take the Guardian's test (conducted by Headon). And only an irregular can visit the Guardian to request to take a Guardian's test (Ch 58). Take note that one cannot become a "chosen one" or an Irregular by participating in the Guardian's test, like Baam's group in the Submerged Fish Hunt test.

The Guardian's test reflect the "worth of the things" the Irregular wants"(Ch 4). How precious are the things he wants which in turn, determines their worth? What are the lengths will the Irregular go to and is he willing to undergo gruelling challenges, in order to take the journey of obtaining them? And as he ascends the Tower, will he give up in the the middle of a test or after taking it?

Upon passing each Guardian's test, the Irregular is then teleported to the next Floor(except for Floor 43 because the Guardian is dead). But if they fail or give up while taking the test, they may not pass and they may not ascend to the next Floor. It is unknown if Irregulars who fail to pass the Guardian's test on a certain Floor are allowed to retake the test or are promptly disqualified. It is supposed an Irregular is then chosen again at the top of the Tower to receive certain powers.

All the known Irregulars that have entered the Tower are famous for being extremely powerful, and have wreaked havoc and terror within the Tower. Their mysterious ability to control and manipulate Shinsoo exceptionally well is also deemed abnormal by the residents of the tower, as Irregulars are capable of having more freedom in controlling Shinsoo even with the restrictions imposed by the laws of the Tower. It is interesting to note that all known Irregulars that have become Rankers have surpassed every single active High Ranker in just one act, Phantaminum storming Zahard's palace, Enryu killing a Guardian, Urek Mazino fighting toe to toe with Arie Hon then being deemed stronger by the latter. It is also interesting to note that none of the known Irregulars have the same position, possibly hinting at the creation of an elite team that could reach the top of the Tower.

Note: Under the current testing system established by the Zahard Empire, the key difference between Regulars and Irregulars is this. Regulars are chosen by Headon and then, instantly teleported to the Second Floor. However, Irregulars simply open the doors of the Tower and are then, teleported to the First Floor to take the Guardian's test (conducted by Headon). That is: they are "unchosen".

Zahard & 10 Great Familes
Although King Zahard and the 10 Great Warriors came into the Tower from the outside world in ancient times, this was before the current testing system was invented. They are not considered as "unchosen Irregulars" because of this.

For now, it is assumed all of them were chosen by the Tower and not Zahard alone, with the rest of them being teleported into the Tower by chance. For the latter, it is assumed on the basis that Irregulars are very rare and if there were really 11 Irregulars, the Guardian of each Floor would simply "choose" one or a few of them instead of letting all of them pass from Floor to Floor.

Known Irregulars

 * Baam (Wave Controller)
 * Phantaminum (Exis)
 * Enryu (Spear Bearer)
 * Urek Mazino (Fisherman)
 * Rachel (Light Bearer) Politically, Rachel is known as an "unchosen Irregular" but to the Guardians, she's most likely not a "chosen one". This is because she lacked certain qualities to be selected by the Tower.