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That won't happen if it's a 1:1 swap. You give your steem tokens to the exchange, and they give you steem/trx tokens back. Two different wallets involved on two different blockchains. More than likely your old stake would either be burned or sold if it survives as a 'classic version'. This would be nothing like a fork of bitcoin, as some people have alluded to.

Drats! Foiled again! ;)