Quirkless people are the people who possess absolutely no Quirk, particularly unique features, or anything that would put them under the classification of being superhuman. They exist as a minority in the My Hero Academia universe, making up approximately 20% of the global population.
Society reacts differently to Quirkless people. In the case of Izuku Midoriya, for example, he was the subject of mockery and prejudice, whereas with Melissa Shield, although she had a good relationship with people with Quirks, she used to be seen with pity for being Quirkless. Commonly, anyone who does not possess a Quirk is considered to be weak and worthless, or that their circumstances are incredibly unfortunate and rare.
It is possible, though highly uncommon, for a Quirkless person to gain a Quirk later in life. One such example of this is them being given a transferable Quirk, such as One For All. However, since they were not born with said Quirk, their body would not be naturally suited to it; because of this, they must train their body in order to be able to use the Quirk properly, similar to how Izuku worked hard to build up enough muscle to use a Quirk that stockpiles large amounts of raw power. Similarly, a person can have a Quirk bestowed upon them through the power-granting Quirk All For One. Unfortunately, some recipients are put into a mindless state due to their inability to handle the physical strain of being given a power through this specific Quirk.
Another, more commonly used method of Quirk attainability is via Quirk-infused DNA injection, which involves an individual being infused with the DNA of a Quirk user, granting the recipient the same power as the donor. One instance is when Kuin Hachisuka, while already possessing a Queen Bee Quirk, injected herself with a blood sample collected from Teruo Unagisawa, allowing her access Teruo's Eel Quirk. However, the recipients don't always acquire the same Quirk efficacy as the progenitor of the Quirk they've obtained. An example of this indifference is the Villain Nine, who was injected with the DNA of another Villain named All For One, granting the former the same ability to steal Quirks from other people, but he was limited to stealing 8 other Quirks.
The trait of Quirklessness appears to be recessive; meaning if at least one parent has a Quirk, that child is more likely to be born with a Quirk, even if the other parent is Quirkless. However, even if both parents are carriers for Quirks, there is still a chance that their child will be born without a Quirk, as seen with Izuku, who didn't inherit either of his parents' Quirks, or even developed an amalgam of their powers.
As seen in the beginning of the series, people who are born with Quirks only have one joint in their pinky toe, suggesting a close chromosomal linkage between the extra toe joint and a lack of a Quirk; people with two joints in their pinky toe are almost always Quirkless.
It is possible for a person to lose their Quirk. The Villain All For One possesses a Quirk that allows him to steal another person's Quirk and use it as his own, leaving the victim Quirkless. Another villain, Nine, possesses a weaker version of this said power but is only able to steal 8 other Quirks.
Another way a person can lose their Quirk is by being subjected to drugs that can damage their Quirk Factor. The Yakuza group, Shie Hassaikai, developed a Quirk-Destroying Drug using the genetic material of girl named Eri, whose Quirk allows her to reverse people back to the way they once were. The drug itself rewinds a person's Quirk Factor back to before the Quirk Phenomenon became a factor of human genetics.
Additionally, if an individual requires a certain body part to activate their Quirk, it is possible to render them functionally "Quirkless" by destroying said anatomy. Kai Chisaki, whose Quirk required the use of his hands, is one such example; after both of his arms were destroyed by Tomura Shigaraki and Mr. Compress, Kai was left unable to activate his own Quirk, despite still technically possessing it.