while(<$fh>)
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is short for

while(defined($_ = <$fh>))
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and $_ is aliased to $a and $b in turn by the foreach loop. Every time you change $_ by assigning a line to it, you change the value of $a or $b.

Solution: Change

    while(<$fh>){
        print;
    }
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to

    local $_;
    while(<$fh>){
        print;
    }
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or

    while(my $line = <$fh>){
        print $line;
    }
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By the way, because $a and $b have special meaning to sort, one usually avoids them. my $a and my $b can actually cause sort to malfunction.