Warning! Spoilers ahead for My Hero Academia chapter 333!
The secret rule that America's top hero Star and Stripe imposed on her own New Order quirk before her confrontation with All For One just changed what everyone thought they knew about these powers in My Hero Academia.
The quirk New Order allows Star and Stripe to change the reality of three objects simultaneously (but she can only alter one rule at a time on herself) so long as certain criteria are met. Aware that All For One might try and steal her quirk, she decreed that New Order will revolt against other quirks before her confrontation with the villain. Of course, All For One eventually steals New Order, and the moment he does, he feels his other quirks "exploding out" in chapter 333. This is important because there have been no documented cases of quirks being destroyed. The unofficial translation of the chapter makes this more clear by having All For One say, "Quirks are either taken...or given...but never destroyed!" Shonen Jump's translator, however, interpreted what the villain says as, "I can only...steal quirks...or bestow them." In other words, he could have known destroying them was possible. He just knew that he couldn't do so himself.
As mentioned above, however, there are no instances that suggest quirks are destructible. If anything, it could just be a theory. If quirks could be destroyed, then the plotline in the third and latest My Hero Academia movie World Heroes' Mission would have been very different. The film's villain Flect Turner is one of the few who initially bought into the unsubstantiated Quirk Doomsday Theory, which foretells that humans will lose control of their quirks, destroying the entire world. As part of his master plan to ensure this doesn't happen, the villain forms the terror organization Humarise, which uses so-called Trigger gas to cause quirk users to lose control of their powers, killing them in the process, all in an effort to herald in a new world free of quirks. If he had known he could destroy quirks, Flect would have undoubtedly found a way. The same can be said of All For One. Neither of them were aware that New Order could supersede the indestructibility of quirks because the United States went out of its way to keep the true capability of the quirk under lock and key.
Up until Star and Stripe's latest stunt, those living in the My Hero Academia universe only knew specific things relating to the known types and subtypes of quirks - and none of them had anything to do with them being destructible. In addition to All For One's ability to add and remove quirks from a user's genetics, there has always been a basic understanding of when they normally manifest, and how the body - even the user's personality - can evolve as a means to both accommodate and allow the power to function properly. Society has also documented hereditary qualities associated with quirks and quirk-related physical aberrations. Additionally, records exist of quirk evolutions that are linked to the Quirk Singulation Theory and how the consciousness of users are contained within quirks.
Whether quirks can be destroyed by means other than Star and Stripe's New Order rule has yet to be realized in My Hero Academia. However, it's quite likely that All For One will use this knowledge he obtained from Star and Stripe's sacrifice to his advantage, especially if he somehow saves his namesake, a quirk that allows him to bestow and rip other quirks from a person's genetics.