The death in Deptford is faked up. The witnesses are all either government agents or professional conmen. The venue belongs to a relative of one of Kit's bosses. The inquest is irregular and the coroner is in on the fix. The body- probably that of a recently executed man- is hastily buried in a common grave. Kit, meanwhile, is on his way out of the country.
The rest is silence. Except that he goes on writing. He may have been in Italy, or Scotland or travelling around; he may have returned to England under a false name. There's no way of knowing. Meanwhile a man called Shakespeare has agreed to put his name to Kit's plays and poems.
Shakespeare is an actor and theatrical entrepreneur. Perhaps he does a bit of writing- botching up old plays and such. (There's a sonnet that puns on the name Hathaway- which doesn't fit with the rest and is altogether pretty feeble; maybe that's an example of Shakespeare's own work.) Anyway this scribbler- who has hitherto written nothing of note- starts producing masterpieces. The man is witty and sociable and smooth. He passes. Not even his closest associates- Ben Jonson for instance- see any reason to question his authorship. The players notice that the scripts he turns in (and this is on the record) are singularly free of corrections and put it down to an extraordinary fluency of invention (Jonson grumbles about it.) Really it's because they're fair copies in Shakespeare's handwriting of Kit's original "foul papers".
The folio collection of "Shakespeare's Works" contains several plays that have never been published before and heavily revised versions of some that have. Maybe Kit has outlived Shakespeare and is still around in the early 1620s- overseeing the production of his magnum opus.
And that's it. No-one guesses. No-one suspects. The man Shakespeare- who, in his lifetime, drew little attention to himself- begins to acquire a legend...
This is summary of other people's research and speculation. I claim none of it as original- except, perhaps, for the sideways glance at the "Hathaway" sonnet.