I'll address the second part of that question first, if I may, although I think some caution needs to be applied to regarding Shakespeare as a 'major figure'.

Shakespeare has become the pre-eminent early modern playwright, but he didn't have that kind of status in his own time. Christopher Marlowe's The Massacre at Paris (c. 1593) was a veritable blockbuster, and Dr Faustus was renowned for terrifying audiences on provincial tours with extra devils appearing on stage, and scenes of hell appearing at the conclusion of the play. Thomas Middleton (a collaborator of Shakespeare's) was also very popular, and a little later, Beaumont and Fletcher's plays were dominating the stage. Shakespeare was part of a milieu of very successful playwrights, and while he was certainly a very successful businessman with a number of well-received plays, it is important not to think of him as being hero-worshipped in his own time the way we do now.

The large number of extant works, and the canonising effect of the Folio have certainly played a huge role in making him the 'major figure' he is today, but that is not to say that there was a widespread sense that his works needed to be preserved for posterity at the time. On the whole, it is very, very common for major works of literature from this period to be lost, and we are pretty lucky that Shakespeare's associates regarded his works as worthy of a folio edition. Marlowe is probably the next-best well known playwright of this period, but many of his texts only survive in very crude copies, and are scarce at that. There is only ONE surviving text of The Massacre at Paris (a play which earned the playhouse owner, Philip Henslowe, a huge sum of money) and the copy that we do have is short and apparently very corrupt. It has garbled, repeated and missing text all over the place. Likewise, Dr Faustus (another play that earned a huge taking when first performed in 1594) exists in two copies, the A-text and the B-text. The A-text is short, and seems like it may have been printed from one of Marlowe's drafts, the B-text looks like it has been extended and revised by later writers. Very few copies of the A-text exist, in spite of the cult popularity of the play.

Printed play texts were usually pretty cheap - they were usually printed in quartos (paper that had been folded a couple of times to get more printed pages out of a single sheet of paper), and there is some evidence to suggest that they weren't regarded as particularly highbrow reading (for example, see the printer's preface to Tamburlaine, where Richard Jones explains that he has taken out 'fond and frivolous gestures' in order to make it more fitting for a gentleman to read 'after your serious affairs and studies'). It's therefore not entirely surprising that cheap books (which were more than likely sold unbound) haven't necessarily survived for 400 years. Copies were lost, fell apart, or simply didn't enjoy large print runs.

Now as for what we know about Cardenio and Love's Labours Won, as is the case with most lost plays of this period, we don't know too much, because it is necessary to rely on fragmentary evidence of their existence. Records of entry into the Stationers' Register (an early version of a copyright office/censor), reports of having viewed the play, or bookseller's records tend to be the main evidence for the existence of lost plays.

In 1598, Francis Meres mentions Love's Labours Won alongside Love's Labours Lost as examples of Shakespeare's proficiency in Comedy, and for a long time, that was our only evidence of that play having ever existed. In 1953, a fragment of a bookseller's list that had been used as part of the binding for another book mentions both Love's Labours Won and Love's Labours Lost, although it doesn't mention the authorship of any of the texts in the list. Taken together, we can assume that is a lost play composed by Shakespeare, but nothing more is known about it (no details of the plot survive). Having been printed, there is still a chance that it may come to light (no first edition of Titus Andronicus was known until 1904, for example).

Cardenio is entered into the Stationers' Register in 1653 as a collaboration between Shakespeare and John Fletcher, and John Heminges (leader of The King's Men players) received payments for 'Cardenno' and 'Cardenna' in 1613. There are no contemporary accounts which elaborate on details of the plot.

However, in 1728, Lewis Theobald published a play called Double Falsehood which he claimed was based on a play originally written by Shakespeare. In 1770 there were some reports that the Museum of the Covent Garden Playhouse held a copy of the manuscript of the play, however, this library was destroyed by fire in 1808. Double Falsehood covers the same plot of the Cardenio episode of Don Quixote with some changes to the story, and it is possible that Theobald's play is based upon an early modern original. Nonetheless, the dialogue is not seen as particularly Shakespeare-an, and it doesn't indicate much more than a glimpse of what Shakespeare's Cardenio would have been like.

Selected Sources:

Shakespeare, William, The Norton Shakespeare, ed. by Stephen Greenblatt, Walter Cohen, Jean E. Howard, and Katharine Eisaman Maus, (New York: W. W. Norton, 2008)

Marlowe, Christopher, The Complete Plays ed. by Frank Romany and Robert Lindsay, (London: Penguin, 2003)

Marlowe, Christopher, The Complete Works of Christopher Marlowe, Vol II: Doctor Faustus, ed by Roma Gill, (Oxford: Oxford University Press, 1990)