You could just use a loop, dealing with each bracketed part that is encountered. Here's a basic technique:

#!/usr/bin/env perl

use strict;
use warnings;

use constant {
    EXTRACTED => 0,
    SUFFIX => 1,
    PREFIX => 2,
};

use Text::Balanced 'extract_bracketed';

my $delim = '([{<';
my $prefix = qr{[^$delim]*};

my $string = 'The (use {of}) parentheses (indicates that the (writer [
+considered] the {information}) less <important—almost> an afterthough
+t).';

my ($current, $wanted) = ($string, '');

while (1) {
    my @parts = extract_bracketed($current, $delim, $prefix);

    if (defined $parts[PREFIX]) {
        my ($trimmed_start) = $parts[PREFIX] =~ /^(.*?)\s*$/;
        $wanted .= $trimmed_start;
    }

    if (defined $parts[EXTRACTED]) {
        $current = $parts[SUFFIX];
    }
    else {
        $wanted .= $parts[SUFFIX];
        last;
    }

}

print "$wanted\n";
[download]

Output:

The parentheses.
[download]

I'll leave you to integrate that technique into your actual production code.

[The lack of sample data — as requested by myself and expanded upon by AnomalousMonk — was disappointing.]

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