To what extent are some of the masks that characters wear in Twelfth Night destroyed by the end of the play?
If we think about it, we can relate your question and the concept of characters wearing masks that allow them to deceive themselves to one of the principal Shakespearian themes, which is appearance vs. reality. Many characters appear or think that they are something other than they are, and by the end of the play have these masks forcefully taken from them and are forced to accept the truth about themselves.
Surely, the major character that this applies to is Malvolio, who, thanks to the ruse of Maria and Sir Toby, thinks that he is something much more than he actually is. It is notable, and somewhat ironic, that, after being a force of sobriety and Puritanism at the beginning of the play, when he is brought out in Act V scene 1 at the end of the play, Olivia refers to him as a "poor fool" that has been "baffled" by the stratagems of Sir Toby and Maria. Malvolio is forced to confront that he is nothing more than a fool who has tried to rise above his station and failed dramatically. His angry response to the otherwise happy crowd reveals his inability to accept his own mistakes and his own identity: "I'll be revenged on the whole pack of you!"
But let us also remember the way that other characters are forced to confront their true identity and realise how they have been deceiving themselves. The love sick Orsino, for example, so consumed with passion for Olivia, realises that the true object of his affection is actually Viola and also realises how over the top his love has been for Olivia. The poor Sir Andrew Aguecheek likewise realises that he has been tricked by Sir Toby into entertaining hopes of a match with Olivia and is forced to accept that he has no chance of ever marrying her. Lastly, Olivia realises how severe her vow of chastity in response to her brother's and father's death was, and also the way that she is tricked by the twins reveals just how foolish she was to make such a strong vow that she could not keep. Masks, and their often forceful removal are a key motif of this brilliant play.