What is the role of the Fool in Shakespeare's King Lear?

The Fool is Lear's own stand-up comedian, sure, but more
interestingly, he's the only guy that Lear allows to criticize him.
(Remember, when Kent lips off, Lear boots him out of the kingdom and when Lear doesn't
like what Cordelia has to say, Lear disowns her altogether.)

As in
many of Shakespeare's plays, the Fool is actually really smart – and the only person who
tells it like it is. Compare Lear's Fool, for example, to Feste in Twelfth
Night – neither one of them are afraid to call their misguided masters
"foolish" and they both function as characters that provide a lot of social commentary.
At the same time, the Fool is more than just a funny and brutally honest guy; he's also
loyal. Along with Kent/Caius, the Fool braves the elements (which at times consist of
rain, thunder, and lightning) with his master.

But the Fool is also a
big mystery: what happens to him? He disappears after Act 3, Scene 6, and nobody ever
explains where he's gone. The only possible reference to the Fool after that is in the
final scene, when King Lear says "And my poor fool is hanged" (5.3.17). This could mean
a couple of things: 1) Lear might be referring to Cordelia with a pet name, "fool,"
since Cordelia has just been hanged by Edmund's goons. 2) Lear could be literally
talking about his Fool – perhaps the Fool was also hanged by Edmund's henchmen or,
perhaps he hung himself out of despair. It's hard to say what really happens to the
Fool. Some literary critics even speculate that the Fool and Cordelia were played by the
same actor. They never appear onstage together, so some scholars hypothesized that the
part was double cast, and that the Fool had to disappear when Cordelia came back into
the play.