The ending...
IT isn't supposed to make literal sense, it's supposed to be emotionally satisfying.
Kauffman dies, but somehow still lives.
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It's supposed to suggest that Andy Kaufman pulled off the world's greatest act of performance art and defied death. Tony Clifton lives while Andy Kaufman in fact died, thus achieving a form of immortality.
It would be analogous to Borat existing after Sacha Baron Cohen's death.