Depending on the complexity of your $target and your data, you may find a gain by breaking your search up:

my $target = shift || 'word';
$target = qr/$target/;
my $re = qr/a=<([^>]+)>/;
while( <DATA> ) {
    next unless /$re/;
    my $s = $1;
    print "[$s]\n" if $s =~ /$target/;
}
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