Note: It's a general misconception Headon teleports outside the Tower to select Regulars. Now that it's revealed Gong Bang resides in the Middle Area and some of its members are also chosen to become Regulars, this makes much more sense when Lero-Ro said that most Regulars come from the Residential Tower (Ch 10).
In this system, Irregulars are called "unchosen Irregulars" and regulars are called "chosen Regulars" or "selected chosen" (,Ch 2). It is unknown if this current selection process is part of a contract Zahard made with a Guardian like Headon and it is assumed Headon's choice reflects the Tower's choice (Ch 2).
They are then likely teleported immediately to the 2nd Floor. (It is unknown if a grace period is given to them or if they're sent immediately to the Inner Tower.)
The relationship between Regulars and non-Regulars is similar to that of the ruling class and the subjected class. This means that Regulars don't have to use any honorifics when addressing non-Regulars. And in turn, Regulars from the Ruling Class don't need to use any honorifics towards Regulars from common families (Source: Author notes from Ch 32).
Climbing the Floors and their RightsEdit
Note: Most of the information in this section was sourced from Ch 79 (Postlogue).
The Regulars must take a series of Tests every time they climb a floor. And due to the difficulty and nature of the complex testing system on the 2nd Floor (Floor of Test), many fail there which means they are stripped of their rights. And the failed Regulars are likely teleported to a Floor or their Floor of origin in the Outer Tower or outside of the Tower after notifying the staff they've finished preparations and are ready to go back home.
When one becomes a chosen Regular and enters the Inner Tower, there is no rule that one must keep their outside name. In fact, most regulars use aliases when registering on either the 2nd Floor or on each Floor (Ch 29) and this likely counts as their right to maintain anonymity or a right to use a name of their choice.
They are also protected under the Tower's Rules upon entering the Inner Tower and in turn, are expected to abide by a set of the Tower's Rules in exchange for this set of rights.
At some point, they likely stop wearing uniforms issued by the Floor and are given the right to wear clothing of their choice.
From the 2nd Floor to the 19th Floor, they get to sleep in dormitories as they aren't allowed to reside in the Middle Area. At the same time, food is probably sold to them as well. Some of the Floors may offer the food for free, as a reward for having passed a certain number of tests.
From the 3rd Floor and on, it's a bit different. Even if they fail, they have the right to retake the tests. Because the difficulty is not that high, they say that most of those who pass the Floor of Test also pass the rest. Most or all tests on a floor are compulsory and you need to pass a test to proceed to the next. This means that if a Regular passed 1 to 2 tests but failed at the next test, he fails the Floor. He has the right to retake the Floor but he must start all over again.
On the 20th Floor, they're chosen once again. Since taking a test requires a lot of points (money) and due to the increase in difficulty, they say there are a lot of Regulars who gave up on the 20th Floor. It's said that even if they've given up, their "premium" status as former regulars helps out a lot in their daily needs.
From the 20th Floor onwards, the right to reside in the Middle Area is granted, so while they dwell in the Middle Area by themselves or with their family, many also take the test after entering the Inner Tower. It can be assumed one is then allowed to buy food of their own choosing, from eateries and restaurants located in the Middle Area.
Currently, many of the characters in the series are Regulars.
Giving up their Regular status and their RightsEdit
Regulars who give up in the middle of climbing the Inner Tower, after they've reached the 3rd Floor, are stripped of their rights and are sent to the Middle Area. They can choose to live there, or move to a lower floor and live on with a new job (Ch 79) like being a support staff to the Testing Director. Of course, depending on how far you've climbed, the way you're treated differs greatly. According to SIU, it's just like "climbing the corporate ladder". Source: ().
But if they belong to outside of the Tower and give up, they are probably teleported back home by Headon or the Guardian of the floor, if they don't want to remain in The Tower. Although it is also possible they aren't permitted to go home at all.
Note: It is unknown if Regulars from the 3rd to 19th Floors are permitted to reside in the Middle Area once they've given up, as they previously didn't have the right to do so. If such former Regulars aren't allowed to live there, then they're likely sent to the Middle Area so they can return home as it can be used to travel between the Inner and Outer Tower.
With the exception of a few (Androssi Zahard and Anak Zahard who were ranked 6E and 10E respectively in Part 1), majority of Regulars are F-Ranked Regulars when they first start out on the 2nd Floor. Once they've passed the 20th Floor, they become an E-Rank Regular.
Based on their performance and score during a test, Regulars earn a certain number of test points which are then used as currency. And these points can be used to purchase meals, drinks and so on. (Ch 31, Ch 55).
It is possible that this practise is enforced only on the 2nd Floor.
It is the most likely that on all of remaining Floor they are using money for their living expenses (You can notice they are using Viole's money for living expenses in Ch. 106: 21F - FUG (1) ).