Fencer: "If you have chip and a chair you can win" is one the most famous lines in poker. In 1982 WSOP Jack Strauss actually came back to win the tournament after being down to just one chip.
You're just not supposed to be out of the game before you really are out of chips. Of course there will be sidepots like in any other all in situation when someone does not have enough to pay BB.
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