Eily has already shown you how to set the options to Text::CSV to parse your data. I'd like to show an alternative: Since it's SQL*, use an SQL parser! Here, I'm using SQL::Statement:

use warnings;
use strict;
use SQL::Statement;
use Data::Dump;

my $sql = <<'END_SQL';
INSERT INTO foo VALUES
(101, '1997-02-25', 'S1', 31.00, NULL, 0.00, 'this becomes two fields,
+ so no go', 5.11),
(102, '1998-03-26', 'S1', 31.00, NULL, 0.00, 'this will remain one fie
+ld', 6.11)
END_SQL

my $parser = SQL::Parser->new();
$parser->{RaiseError}=1;
my $stmt = SQL::Statement->new($sql,$parser);
dd $stmt->row_values;

__END__

(
  [
    101,
    "1997-02-25",
    "S1",
    "31.00",
    undef,
    "0.00",
    "this becomes two fields, so no go",
    5.11,
  ],
  [
    102,
    "1998-03-26",
    "S1",
    "31.00",
    undef,
    "0.00",
    "this will remain one field",
    6.11,
  ],
)
[download]

Update: * Hmm, at least it looks more like SQL than CSV to me, although you did say it's a "MySql CSV/dump".