The real Falstaff
In the first version of Shakespeare's Henry IV, Part One, the character now known as Falstaff was called Sir John Oldcastle. The historical Oldcastle was an old friend of the king's--but he bore no resemblance to Shakespeare's character. There is likewise no historical evidence of Henry's wild youth as depicted in the play; his only controversial action was disagreeing with his father over policy in France, as a result of which he was expelled from the Council.
In one of Shakespeare's probable sources, an anonymous play called The Famous Victories of Henry the Fifth, there is a boisterous character called Jock Oldcastle, and much play on the legend of Hal's wild youth.
What's in a name?
The name may have been changed under protest from one of Oldcastle's descendents (the current Lord Chamberlain was one).
A pun in the play still relies on the original name of the character: Hal refers to Falstaff as "my old lad of the castle" (1.2.42). The first edition of text of the new Oxford edition of the plays restored the name Oldcastle (though it was never used in any of the published editions).
What kind of death is being portrayed in the illustration?*
Footnotes
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"The hanging of Sir John Oldcastell"
Aboute the same season, was sir John Oldcastell, Lord Cobham taken . . . not without daunger and hurtes of some that were at the taking of him, for they could not take him, till he was wounded himselfe. . . . in the end he was condemned, and finally was drawen from the tower unto S. Giles fielde, and there hanged in a chayne by the midle, and after consumed with fire, the gallawes and all.
(Quoted from the site at the University of Pennsylvania on Holinshed.)