Creator Breakdown: Shakespeare's only son, Hamnet, died at the age of eleven. Harold Bloom, Bill Bryson, and Stephen Greenblatt (among others) all speculate that Shakespeare's grief over his son seeped into his plays - from Constance's monologue mourning her son in King John, to the ecstatic scene of the twins reuniting when each thought the other dead in Twelfth Night (Hamnet was the fraternal twin to Judith), and, especially, Shakespeare's tragedy of sons, fathers, and legacies, Hamlet.
Missing Episode: Records indicate that Shakespeare wrote plays entitled The History of Cardenio and Love Labour's Won (which is probably a sequel or something along those lines to Love's Labour's Lost). Unfortunately, no copies of them are known to exist.
An 18th-century play called Double Falsehood is thought to be a rewrite of Cardenio (it has the same plot as the Cardenio episode in Don Quixote only with the names changed) and was included in the Arden Shakespeare series in 2010. Arden credited the work to Shakespeare, John Fletcher (who appears to have collaborated with Shakespeare on the play or rewrote the play from Shakespeare's original script), and eighteenth-century dramatist and editor Lewis Theobald. Theobald claimed to have adapted the text from a Restoration-era manuscript which was at least based on the Shakespeare/Fletcher original (Restoration productions of Shakespeare were heavily adapted for contemporary tastes and theatrical practices) but which was later destroyed in a fire. Understandably, people at the time doubted this, and that was largely that until the 2010s, by which time computer-based lexical analysis and interest in Shakespeare's collaborative work led scholars to revisit Theobald's claims and determine that he may have been telling the truth. While the surviving text of The Double Falsehood is probably an adaptation of an adaptation, it may well have its origins in Shakespeare.
Love's Labour's Won is sometimes argued to have been an alternate title to an extant play (following the example of Twelfth Night, or What You Will) — the most frequently suggested candidates are The Taming of the Shrew and Much Ado About Nothing, as they are not mentioned in the 1598 pamphlet that is the only evidence that Love's Labour's Won existed, were probably written before 1598, and could theoretically be described by the title. The Royal Shakespeare Company staged Much Ado under that title in 2014, alongside Love's Labour's Lost with the same cast. However, Love's Labour's Lost does end with an obvious Sequel Hook so any attempt to connect it to an existing play is purely conjectural.
Reality Subtext: Some scholars have theorized about the dynamic of Shakespeare's company via reading the plays to explain some of some of plays' quirks. For example, Shakespeare is assumed to have fallen out with Will Kempe, the company clown, for his constant improvisations and audience-mugging, due to Falstaff (one of his most famous roles) dying offstage in Henry V and due to the diatribe against ad-libbing clowns in Hamletnote (though in this scene Hamlet wants the players to understand how dangerous it would be to ad-lib during Hamlet's rewrite of the play). It is known from historical records that Kemp, an otherwise high-ranking stakeholder in Shakespeare's Company, suddenly left for some reason. Shakespeare's bad experiences with Kempe probably explains why he hired Robert Armin, who plays a more subdued and intelligent Sad Clown-type character (his most famous role probably being Feste from Twelfth Night). Shakespeare wrote Hamlet with Richard Burbage in mind, which would explain why the character is middle aged when the original character was a teenager.