If you do not want the last value, return something else:

sub mySub {
    if ($R) {
        return;
    } else {
        print "CONDITION WORKS\n";
        $R = "some string\n";
    }
}
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Usually, your subroutine should return a value and not print anything, or it should print something, but then you should call it in a void context (or a boolean one, checking for success). Making it both print and return a value to be printed makes it harder for reuse.